BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andreas Petersson (University of Oslo) DTSTART:20200918T090000Z DTEND:20200918T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/1 DESCRIPTION:Title: Finite element approximation of Lyapunov equations for the co mputation of quadratic functionals of SPDEs\nby Andreas Petersson (Uni versity of Oslo) as part of STAR seminars\n\n\nAbstract\nWe consider the c omputation of quadratic functionals of the solution to a linear parabolic stochastic partial differential equation (SPDE) with multiplicative Gaussi an noise on a bounded domain. The functionals are allowed to be path depen dent and the noise is white in time and may be white in space. An operator valued Lyapunov equation\, whose solution admits a deterministic represen tation of the functional of the SPDE solution\, is used for this purpose a nd error estimates are shown in suitable operator norms for a fully discre te approximation of this equation. We also use these estimates to derive w eak error rates for a fully discrete approximation of the SPDE itself. In the setting of finite element approximations\, a computational complexity comparison reveals that approximating the Lyapunov equation allows us to c ompute quadratic functionals more cheaply compared to applying Monte Carlo or covariance-based methods directly to the discretized SPDE. We illustra te the theoretical results with numerical simulations.\nThis is joint work with Adam Andersson\, Annika Lang and Leander Schroer.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Emel Savku (University of Oslo) DTSTART:20200925T090000Z DTEND:20200925T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/2 DESCRIPTION:Title: Optimal investment strategies in a Markov Regime-Switching Ma rket\nby Emel Savku (University of Oslo) as part of STAR seminars\n\n\ nAbstract\nWe discuss two optimal investment problems by using zero-sum an d nonzerosum stochastic game approaches in a continuous-time Markov regime switching jump-diffusion environment. We represent different states of an economy by a D-state Markov chain. The first application is a zero-sum gam e between an investor and the market\, and the second one formulates a non zerosum stochastic differential portfolio game as the sensitivity of two i nvestors’ terminal gains.We derive regime-switching Hamilton–Jacobi– Bellman–Isaacs equations and obtain explicit optimal portfolio strategie s.We illustrate our results in a two-state special case and observe the im pact of regime switches by comparative results.\nJoint work with Gerhard W ilhem Weber.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Jasmina Djordjevic (University of Oslo) DTSTART:20201002T090000Z DTEND:20201002T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/3 DESCRIPTION:Title: Perturbation effect on Reflected Backward Stochastic Differen tial Equations\nby Jasmina Djordjevic (University of Oslo) as part of STAR seminars\n\n\nAbstract\nPerturbed stochastic differential equations\, in general\, are the topic of permanent interest of many authors\, both t heoretically and in applications. Stochastic models of complex phenomena u nder perturbations in analytical mechanics\, control theory and population dynamics\, for example\, can be sometimes compared and approximated by ap propriate unperturbed models of a simpler structure. In this way\, the pro blems can be translated into more simple and familiar cases which are easi er to solve and investigate. Problems of perturbed backward stochastic dif ferential equations (BSDEs) are very interesting because of their applicat ions in economy and finance. The most interesting problem in this field of perturbations of BSDEs deals with a large class of reflected backward sto chastic differential equations whose generator\, barrier process and final condition are arbitrarily dependent on a small parameter. The solution of perturbed equation\, is compared in the L p -sense\, with the solutions o f the appropriate unperturbed equations. Conditions under which the soluti on of the unperturbed equation is L p -stable are given. It is shown that for an arbitrary η > 0 there exists an interval [t(η)\, T] ⊂ [0\, T] o n which the L p -difference between the solutions of both the perturbed an d unperturbed equations is less than η.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonardo Rydin Gorjão (Institute of Theoretical Physics\, Univers ity of Cologne) DTSTART:20201009T090000Z DTEND:20201009T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/4 DESCRIPTION:Title: Applications and developments of stochastic processes in powe r-grid frequency measurements: A data-driven study.\nby Leonardo Rydin Gorjão (Institute of Theoretical Physics\, University of Cologne) as par t of STAR seminars\n\n\nAbstract\nPower-grid frequency is a key measuremen t of stability of power-grid systems. It comprises the balance of power ge neration and consumption\, electricity market exchanges\, and control mech anism. Power-grid frequency\, as stochastic process\, has been scarcely st udied. We will present the developments in power-grid frequency data colle ction\, the design of a N-dimensional non-parametric estimator for time-co ntinuous Markov processed\, and the design of a computationally efficient Multifractal Detrended Fluctuation Analysis (MFDFA) algorithm. Lastly\, we will report on the design of a surrogate stochastic model for power-grid frequency via a fractional Ornstein–Uhlenbeck process\, the application of a Hurst index and a volatility estimator\, and the limitations due to m ultifractional and time-and-space coloured noise.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Marta Sanz-Solé (University of Barcelona) DTSTART:20201016T090000Z DTEND:20201016T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/5 DESCRIPTION:Title: Stochastic wave equations with super-linear coefficients\ nby Marta Sanz-Solé (University of Barcelona) as part of STAR seminars\n\ n\nAbstract\nWe consider a stochastic wave equation on R^d \, d ∈ {1\, 2 \, 3}\, driven by a Gaussian noise in (t\, x)\, white in time. We assume t hat the free terms b and σ are such that\, for |x| → ∞\, \n|σ(x)| ≤ σ_1 + σ2_|x| (ln_+(|x|))^a \, |b(x)| ≤ θ_1 + θ_2|x| (ln_+(|x|))^ δ \, (1) \nwhere θ_2\, σ_2 > 0\, δ\, a > 0\, with b dominating over σ . For any fixed time horizon T > 0 and with a suitable constraints on the parameters a\, δ\, σ_2 and θ_2\, we prove existence of a random field s olution to the equation and that this solution is unique\, and bounded in time and in space a.s. The research is motivated by the article [R. Dalang \, D. Khoshnevisan\, T. Zhang\, AoP\, 2019] on a 1-d reaction-diffusion eq uation with coefficients satisfying conditions similar to (1). We see that the L^∞- method used by these authors can be successfully implemented i n the case of wave equations. This is joint work with A. Millet (U. Paris 1\, Panthéon-Sorbonne)​.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Samy Tindel (Purdue University) DTSTART:20201023T090000Z DTEND:20201023T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/6 DESCRIPTION:Title: A coupling between Sinai’s random walk and Brox diffusion\nby Samy Tindel (Purdue University) as part of STAR seminars\n\n\nAbstr act\nSinai’s random walk is a standard model of 1-dimensional random wal k in random environment. Brox diffusion is its continuous counterpart\, th at is a Brownian diffusion in a Brownian environment. The convergence in l aw of a properly rescaled version of Sinai’s walk to Brox diffusion has been established 20 years ago. In this talk\, I will explain a strategy wh ich yields the convergence of Sinai’s walk to Brox diffusion thanks to a n explicit coupling. This method\, based on rough paths techniques\, opens the way to rates of convergence in this demanding context. Notice that I ’ll try to give a maximum of background about the objects I’m manipula ting\, and will keep technical considerations to a minimum.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Yaozhong Hu (University of Alberta) DTSTART:20201106T100000Z DTEND:20201106T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/7 DESCRIPTION:Title: Functional central limit theorems for stick-breaking priors\nby Yaozhong Hu (University of Alberta) as part of STAR seminars\n\n\nA bstract\nWe obtain the empirical strong law of large numbers\, empirical \ nGlivenko-Cantelli theorem\, central limit theorems\, \nfunctional central limit theorems for various nonparametric Bayesian priors\nwhich include the Dirichlet process with general stick-breaking weights\, \nthe Poi sson-Dirichlet process\, the normalized inverse Gaussian \nprocess\, the normalized generalized gamma \nprocess\, and the generalized Diri chlet process. \nFor the Dirichlet process with general stick-breaking we ights\, \nwe introduce two general conditions such that the central limit theorem holds. \nExcept in the case of generalized Dirichlet process\, si nce the finite dimensional \ndistributions of these processes are either h ard to obtain or are \ncomplicated to use even they are available\, \nwe use the general moment method to obtain the convergence results. \nFor t he generalized Dirichlet process we use its finite dimensional marginal d istributions to obtain the asymptotics although \nthe computations are h ighly technical.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Rama Cont (University of Oxford) DTSTART:20201113T100000Z DTEND:20201113T111500Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/8 DESCRIPTION:Title: Excursion risk\nby Rama Cont (University of Oxford) as pa rt of STAR seminars\n\n\nAbstract\nA broad class of dynamic trading strate gies may be characterized in terms of excursions of the market price of a portfolio away from a reference level. We propose a mathematical framew ork for the risk analysis of such strategies\, based on a description in terms of price excursions\, first in a pathwise setting\, without probabil istic assumptions\, then in a probabilistic setting\, when the price is mo delled as a Markov process.\n\nWe introduce the notion of δ-excursion\, d efined as a path which deviates by δ from a reference level before retur ning to this level. We show that every continuous path has a unique decomp osition into such δ-excursions\, which turn out to be useful for the scen ario analysis of dynamic trading strategies\, leading to simple expression s for the number of trades\, realized profit\, maximum loss and drawdown. \nWhen the underlying asset follows a Markov process\, we combine these re sults with Ito's excursion theory to obtain a tractable decomposition of t he process as a concatenation of independent δ-excursions\, whose distrib ution is described in terms of Ito's excursion measure. We provide analyti cal results for linear diffusions and give new examples of stochastic pro cesses for flexible and tractable modeling of excursions. Finally\, we des cribe a non-parametric scenario simulation method for generating paths who se excursions match those observed in a data set.\n\nThis is joint work wi th: Anna Ananova and RenYuan Xu.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Federica Masiero (University of Milano-Bicocca) DTSTART:20201218T100000Z DTEND:20201218T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/9 DESCRIPTION:Title: Regularizing properties and HJB equations for stochastic prob lems with delay\nby Federica Masiero (University of Milano-Bicocca) as part of STAR seminars\n\n\nAbstract\nIn this talk we consider stochastic differential equations with delay.\nIt is well known that the Ornstein-Uhl enbeck transition semigroup doesn’t have regularizing properties\, such as the strong Feller property. So in general\, the associated Hamilton-Jac obi-Bellman (HJB) equation cannot be solved in mild sense by a classical f ixed point argument. We present a result of existence of regular solutions for the HJB equations related to a stochastic controlled equation with de lay in the control and in the case when\, as it often occurs in applicatio ns\, the objective function depends only on the “present” of the state and control variable. The result is based on partial regularization resul ts for the associated Ornstein-Uhlenbeck semigroup.\nIn analogy\, we inves tigate partial reularizing properties in the case of delay in the state an d with a special dependence on the past trajectory\, and we solve in mild sense the associated HJB equation and the stochastic controlled problem re lated.\n\nThe talk is mainly based on joint works with F. Gozzi and G. Tes sitore.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Tusheng Zhang (University of Manchester) DTSTART:20201120T100000Z DTEND:20201120T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/10 DESCRIPTION:Title: Reflected Brownian motion with measure-valued drifts\nby Tusheng Zhang (University of Manchester) as part of STAR seminars\n\n\nAb stract\nIn this talk\, I will present some recent results on the uniquenes s and existence of weak solution to the reflected Brownian motion with me asure-valued drifts. Furthermore\, we obtain some Gaussian type estimates of the transition density function of the solution and we also provide solutions to the associated Neumann boundary value problems.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/10/ END:VEVENT BEGIN:VEVENT SUMMARY:David Ruiz Banos (University of Oslo) DTSTART:20201204T100000Z DTEND:20201204T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/11 DESCRIPTION:Title: Life and pension insurance policies with random cash flows s ubject to interest rate regimes\nby David Ruiz Banos (University of Os lo) as part of STAR seminars\n\n\nAbstract\nA life or pension insurance is a contract between an insurance company and a person\, where the insurer promises to pay a sum of money\, either at once or periodically\, to the i nsured or a beneficiary (e.g. family member) under some specified events. Actuaries must assess the value of such contracts and their risk. For exam ple\, how much is it worth today a pension agreement for a 30 year old Nor wegian citizen consisting of a yearly pension of NOK200 000 from a retirem ent age of 70 years? This question\, although it may seem easy to answer\, is not. There are two main risks for such contract from the insurance com pany perspective. First\, interest rate risk (too low/high interest) and l ogenvity or mortality risk (wrong forecast of mortality).\n\nIn this talk we will discuss interest rate risk and derive a formula for the value of i nsurance contracts where the cash flow (e.g. NOK200 000) is also random\, and not fixed. For example: a pension which pays NOK200 000 in high intere st rate regimes and NOK150 000 in low interest rate regimes.\nWe will intr oduce the main and basic definitions and concepts for those who are not ac quainted with it. Then we will derive the so-called Thiele's partial diffe rential equation for computing prospective reserves and finally we will lo ok at specific examples under the Vasicek model by either solving the prob lem explicitly (tedious but worth it) or numerically (implicit and explici t finite difference method).\nFinally\, we will also overview some possibl e open questions and future research plans.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Arne Bang Huseby (University of Oslo) DTSTART:20210115T100000Z DTEND:20210115T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/12 DESCRIPTION:Title: Optimal reinsurance contracts in the multivariate case\n by Arne Bang Huseby (University of Oslo) as part of STAR seminars\n\n\nAbs tract\nAn insurance contract implies that risk is ceded from ordinary poli cy holders to companies. However\, companies do the same thing between th emselves. This is known as reinsurance\, and the ceding company is known as the cedent. The rationale could be the same\; i.e.\, that a financiall y weaker agent is passing risk to a stronger one. In reality even the larg est companies do this to diversify risk\, and financially the cedent may b e as strong as the reinsurer. The problem of determining re­in­su­ranc e contracts which are optimal with respect to some reasonable criterion ha s been studied extensively within actuarial science. Different contact ty pes are considered such as stop-loss contracts where the reinsurance compa ny covers risk above a certain level\, and insurance layer contracts where the reinsurance company covers risk within an interval. The contracts ar e then optimized with respect to some risk measure\, such as value-at risk (VaR) or conditional tail expectation (CTE).\nIn this seminar we consider the problem of minimizing VaR in the case of multiple insurance layer con tracts. Such contracts are known to be optimal in the univariate case\, a nd the optimal contract is easily determined. In the multivariate case\, however\, finding the optimal set of contracts is not easy. In fact the o ptimal contract is not even unique in this case. Still by considering sol utions where the risk is balanced between the contracts\, a solution can b e found using an iterative Monte Carlo method.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Josep Vives (University of Barcelona) DTSTART:20210129T100000Z DTEND:20210129T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/13 DESCRIPTION:Title: Decomposition and high order approximation of option prices. Some applications to Heston\, Bates\, CEV and rough volatility models \nby Josep Vives (University of Barcelona) as part of STAR seminars\n\n\nA bstract\nUsing Itô calculus techniques we present an option price decompo sition for local and stochastic volatility jump diffusion models and we us e it to obtain fast and accurate approximations of call option prices for different local or stochastic volatility models.\n\nThe main purpose is to present the ideas given in the recent paper:\n\nA. Gulisashvili\, M. Lagu nas\, R. Merino and J. Vives (2020): “Higher order approximation of call option prices in stochastic volatility models”. Journal of Computationa l Finance 24 (1).\n\nBut I will also comment ideas of the papers:\n\nE. Al òs\, R. De Santiago and J. Vives (2015): “Calibration of stochastic vol atility models via second order approximation: the Heston case”. Interna tional Journal of Theoretical and Applied Finance 18 (6): 1550036 (31 page s).\n\nJ. Vives (2016): “Decomposition of the pricing formula for stocha stic volatility models based on Malliavin – Skorohod type calculus”. P roocedings of the Research School CIMPA-UNESCO-MSER-MINECO-MOROCCO on Stat istical Methods and Applications in Actuarial Science and Finance 2013. Sp ringer.\n\nR. Merino and J. Vives (2017): “Option price decomposition in local volatility models and some Applications”. International Journal o f Stochastic Analysis. Volume 2017\, Article ID 8019498\, 16 pages\n\nR. M erino\, J. Pospísil\, T. Sobotka and J. Vives (2018): “Decomposition fo rmula for jump diffusion models”. International Journal of Theoretical a nd Applied Finance 21 (8).\n\nR. Merino\, J. Pospisil\, T. Sobotka\, T. So ttinen and J. Vives (2021): “Decomposition formula for rough Volterra st ochastic volatility models”. Submitted.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Emil R. Framnes (Global Head of Trading Norges Bank Investment Man agement) DTSTART:20210212T100000Z DTEND:20210212T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/14 DESCRIPTION:Title: Equity trading at NBIM\nby Emil R. Framnes (Global Head of Trading Norges Bank Investment Management) as part of STAR seminars\n\n \nAbstract\nEmil will give an introduction to Norges Bank Investment Manag ement and its trading operations. His presentation will mainly focus on tr ading in equity markets and feature some of the dynamics and characteristi cs of the equity market and explain how various participants like institut ional managers\, high frequency traders and retail clients trade and shape equity markets today.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Nacira Agram (Linnaeus University) DTSTART:20210219T100000Z DTEND:20210219T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/15 DESCRIPTION:Title: Deep learning and stochastic mean-field control for a neural network model\nby Nacira Agram (Linnaeus University) as part of STAR seminars\n\n\nAbstract\nWe study a membrane voltage potential model by mea ns of stochastic control of mean-field stochastic differential equations and by machine learning techniques. The mean-field stochastic control prob lem is a new type\, involving the expected value of a combination of the s tate X(t) and the running control u(t) at time t. Moreover\, the control i s two-dimensional\, involving both the initial value z of the state and th e running control u(t).\nWe prove a necessary condition for optimality and a verification theorem of a control (u\; z) for such a general stochastic mean-field problem. The results are then applied to study a particular ca se of a neural network problem\, where the system has a drift given by E[u (t)X(t)] and the problem is to arrive at a terminal state value X(T) which is close in terms of variance to a given terminal value F under minimal c osts\, measured by z^2 and the integral of u^2(t).\nThis problem is too co mplicated to handle by mathematical methods alone. We solve it using deep learning techniques.\nThe talk is based on joint work with A. Bakdi and B. Øksendal at University of Oslo.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Annika Lang (Chalmers University of Technology) DTSTART:20210305T100000Z DTEND:20210305T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/16 DESCRIPTION:Title: The stochastic wave equation on the sphere: properties and s imulation\nby Annika Lang (Chalmers University of Technology) as part of STAR seminars\n\n\nAbstract\nThe stochastic wave equation driven by iso tropic Gaussian noise is considered on the unit sphere. We solve this stoc hastic partial differential equation and discuss properties of the derived solutions. These are used in the developed approximation scheme based on spectral methods and its convergence analysis. We derive strong\, weak\, a nd almost sure convergence rates for the proposed algorithm and show that these rates depend only on the smoothness of the driving noise\, the initi al conditions\, and the test functions. Numerical experiments confirm the theoretical rates. Finally we discuss extensions to more general domains a nd equations that can be treated in a similar way.\nThis talk is based on joint work with David Cohen\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Lobbe (University of Oslo) DTSTART:20210319T100000Z DTEND:20210319T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/17 DESCRIPTION:Title: Pathwise approximations for the solution of the non-linear f iltering problem\nby Alexander Lobbe (University of Oslo) as part of S TAR seminars\n\n\nAbstract\nStochastic Filtering deals with the recovery o f the state of a signal process from noisy observations.\nFiltering models are ubiquitous within science and engineering\, weather prediction being only one important example. In such applications\, accurate\, fast\, and s table algorithms for the approximation of the filtering functional are ess ential.\nAfter introducing the stochastic filtering framework\, we conside r high order approximations of the solution of the stochastic filtering pr oblem and derive their pathwise representation in the spirit of earlier wo rk by Clark and Davis. The robustness property of the derived approximatio n is subsequently proved. Thus\, we establish that the high order discreti sed filtering functionals can be represented by Lipschitz continuous funct ions defined on the observation path space.\nJoint work with Dan Crisan an d Salvador Ortiz-Latorre\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Lyudmila Grigoryeva (University of Kostanz) DTSTART:20210430T090000Z DTEND:20210430T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/18 DESCRIPTION:Title: Discrete-time signatures and randomness in reservoir computi ng\nby Lyudmila Grigoryeva (University of Kostanz) as part of STAR sem inars\n\n\nAbstract\nA new explanation of geometric nature of the reservoi r computing phenomenon is presented. Reservoir computing is understood in the literature as the possibility of approximating input/output systems wi th randomly chosen recurrent neural systems and a trained linear readout l ayer. Light is shed on this phenomenon by constructing what is called stro ngly universal reservoir systems as random projections of a family of stat e-space systems that generate Volterra series expansions. This procedure y ields a state-affine reservoir system with randomly generated coefficients in a dimension that is logarithmically reduced with respect to the origin al system. This reservoir system is able to approximate any element in the fading memory filters class just by training a different linear readout f or each different filter. Explicit expressions for the probability distrib utions needed in the generation of the projected reservoir system are stat ed and bounds for the committed approximation error are provided.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Arne Løkka (London School of Economics) DTSTART:20210416T090000Z DTEND:20210416T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/19 DESCRIPTION:Title: Foreign exchange equilibrium\, international trade and tradi ng costs\nby Arne Løkka (London School of Economics) as part of STAR seminars\n\n\nAbstract\nIn this paper we prove existence and uniqueness of an equilibrium for an international economy consisting of two separate ec onomies and a complete financial market. Each economy produce a single per ishable good and trade between the two economies carries proportional trad ing costs. In each economy there are a number of agents aiming to maximise their expected utility of consumption of the single perishable good. We d raw on the methods used for the one economy case using the Negishi argumen t\, and obtain semi-explicit formulas for the equilibrium solutions. In or der to prove uniqueness\, we establish that for any equilibrium\, the cons umptions must be Pareto optimal. To account for the costs of trading betwe en the economies\, this requires a modification of the standard notion of feasible allocations and Pareto optimality.\n\nOur results therefore gener alise the theory for the one economy in a number of interesting ways that offer new insights and perspectives. \nModels of international economies w ith proportional trading costs have received a lot of attention in economi cs\, but as far as we know\, existence and uniqueness of an equilibrium ha ve not rigorously been established.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Dan Crisan (Imperial College London) DTSTART:20210507T090000Z DTEND:20210507T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/20 DESCRIPTION:Title: Well-posedness Properties for a Stochastic Rotating Shallow Water Model\nby Dan Crisan (Imperial College London) as part of STAR s eminars\n\n\nAbstract\nThe rotating shallow water (RSW) equations describe the evolution of a compressible rotating fluid below a free surface. The typical vertical length scale is assumed to be much smaller than the horiz ontal one\, hence the shallow aspect. The RSW equations are a simplificati on of the primitive equations which are the equations of choice for modell ing atmospheric and oceanic dynamics. In this talk\, I will present some well-posedness properties of a viscous rotating shallow water system. The system is stochastically perturbed in such a way that two key properties o f its deterministic counterpart are preserved. First\, it retains the char acterisation of its dynamics as the critical path of a variational problem . In this case\, the corresponding action function is stochastically pertu rbed. Secondly\, it satisfies the classical Kelvin circulation theorem. T he introduction of stochasticity replaces the effects of the unresolved sc ales. The stochastic RSW equations are shown to admit a unique maximal st rong solution in a suitably chosen Sobolev space which depends continuousl y on the initial datum. The maximal stopping time up to which the solution exist is shown to be strictly positive and\, for sufficiently small init ial datum\, the solution is shown global in time with positive probability . This is joint work with Dr Oana Lang (Imperial College London) and forms part of the ERC Synergy project “Stochastic transport in upper ocean dy namics”\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Lord (Radboud University) DTSTART:20210521T090000Z DTEND:20210521T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/21 DESCRIPTION:Title: Adaptive time-stepping for S(P)DEs​\nby Gabriel Lord ( Radboud University) as part of STAR seminars\n\n\nAbstract\nWe present how adaptive time-stepping might be used to solve SDEs with non-Lipschitz dri ft (and potentially diffusion) combined with a tamed or similar method. We illustrate how to pick the timestep and look at strong convergence. We t hen consider the extension to stochastic PDEs and will mention the two cas es of additive and multiplicative noise and illustrate the results numeric ally.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrey Dorogovtsev (National Academy of Science of Ukraine) DTSTART:20210611T090000Z DTEND:20210611T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/22 DESCRIPTION:Title: Occupation and evolutionary measure-valued processes\nby Andrey Dorogovtsev (National Academy of Science of Ukraine) as part of ST AR seminars\n\n\nAbstract\nn the talk we consider two types of measure-val ued processes constructed from the processes on the phase space. These are visitation processes and solutions to equations with interactions. We wil l discuss questions of stability and stochastic calculus for such processe s. Applications to construction of loop eraised random walks are presented .\nThe talk is based on the joint work with Iryna Nishchenko and Jasmina Đorđević.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Ralf Korn (University of Kaiserslautern) DTSTART:20210820T090000Z DTEND:20210820T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/23 DESCRIPTION:Title: Least-Squares MC for Proxy Modeling in Life Insurance: Linea r Regression and Neural Networks\nby Ralf Korn (University of Kaisersl autern) as part of STAR seminars\n\n\nAbstract\nThe Solvency Capital Requi rement (SCR) is the amount of Available Capital that an insurer has to pro vide to be solvent by the end of the year with a probability of (at least) 99.5%. Due to regulations\, the SCR should be calculated from the distrib ution of the one-year loss if the insurer uses an interal model. Given th e complicated cash flow projections of a life insurer\, this calculation i s a tremendous task and cannot be performed by a crude Monte Carlo approac h. In this talk\, we show how to overcome computational complexity by usin g the so called least-squares Monte Carlo approach in combination with bot h linear regression and a feedforward neural network. Here\, it is particu larly challenging to obtain the so-called ground truth to calibrate our mo dels.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefano De Marco (Ecole Polytechnique Palaiseau) DTSTART:20210917T090000Z DTEND:20210917T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/24 DESCRIPTION:Title: On the implied and local volatility surfaces generated by ro ugh volatility\nby Stefano De Marco (Ecole Polytechnique Palaiseau) as part of STAR seminars\n\n\nAbstract\nSeveral asymptotic results for the i mplied volatility generated by a rough volatility model have been obtained in recent years (notably in the small-maturity regime)\, providing a bett er understanding of the shapes of the volatility surface induced by such m odels\, and supporting their calibration power to SP500 option data.\nRoug h volatility models also generate a local volatility surface\, via the Mar kovian projection of the stochastic volatility (equivalently\, via Dupire' s formula applied to the model's option price surface). We complement the existing results with the asymptotic behavior of the local volatility surf ace generated by a class of rough stochastic volatility models encompassin g the rough Bergomi model.\nNotably\, we observe that the celebrated "1/2 skew rule" linking the short-term at-the-money (ATM) skew of the implied v olatility to the short-term ATM skew of the local volatility\, a consequen ce of the celebrated "harmonic mean formula" of [Berestycki\, Busca\, and Florent\, QF 2002]\, is replaced by a new rule: the ratio of the implied v olatility and local volatility ATM skews tends to the constant 1/(H + 3/2) (as opposed to the constant 1/2)\, where H is the regularity index of the underlying instantaneous volatility process.\nJoint work with Florian Bo urgey\, Peter Friz\, and Paolo Pigato.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Mathieu Rosenbaum (Ecole Polytechnique Palaiseau) DTSTART:20211001T090000Z DTEND:20211001T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/25 DESCRIPTION:Title: A rough volatility tour from market microstructure to VIX op tions via Heston and Zumbach.\nby Mathieu Rosenbaum (Ecole Polytechniq ue Palaiseau) as part of STAR seminars\n\n\nAbstract\nIn this talk\, we pr esent an overview of recent results related to the rough volatility paradi gm. We consider both statistical and option pricing issues in this framewo rk. We notably connect the behaviour of high frequency prices to that of i mplied volatility surfaces\, even for complex products such as the VIX.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Blanka Hovarth (King's College London) DTSTART:20210903T090000Z DTEND:20210903T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/26 DESCRIPTION:Title: Data-Driven Market Simulators some simple applicatons of sig nature kernel methods in mathematical finance\nby Blanka Hovarth (King 's College London) as part of STAR seminars\n\n\nAbstract\nTechniques that address sequential data have been a central theme in machine learning res earch in the past years. More recently\, such considerations have entered the field of finance-related ML applications in several areas where we fac e inherently path dependent problems: from (deep) pricing and hedging (of path-dependent options) to generative modelling of synthetic market data\, which we refer to as market generation.\nWe revisit Deep Hedging from the perspective of the role of the data streams used for training and highlig ht how this perspective motivates the use of highly accurate generative mo dels for synthetic data generation. From this\, we draw conclusions regard ing the implications for risk management and model governance of these app lications\, in contrast torisk-management in classical quantitative financ e approaches.\nIndeed\, financial ML applications and their risk-managemen t heavily rely on a solid means of measuring and efficiently computing (sm ilarity-)metrics between datasets consisting of sample paths of stochastic processes. Stochastic processes are at their core random variables with v alues on path space. However\, while the distance between two (finite dime nsional) distributions was historically well understood\, the extension of this notion to the level of stochastic processes remained a challenge unt il recently. We discuss the effect of different choices of such metrics wh ile revisiting some topics that are central to ML-augmented quantitative f inance applications (such as the synthetic generation and the evaluation o f similarity of data streams) from a regulatory (and model governance) per pective. Finally\, we discuss the effect of considering refined metrics wh ich respect and preserve the information structure (the filtration) of the marketand the implications and relevance of such metrics on financial res ults.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Galinberti (NTNU Trondheim) DTSTART:20211015T090000Z DTEND:20211015T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/27 DESCRIPTION:Title: Neural Networks in Fréchet spaces\nby Luca Galinberti ( NTNU Trondheim) as part of STAR seminars\n\n\nAbstract\nIn this talk we pr esent some novel results obtained by Fred Espen Benth (UiO)\, Nils Deterin g (University of California Santa Barbara) and myself on abstract neural n etworks and deep learning. More precisely\, we derive an approximation res ult for continuous functions from a Fréchet space $X$ into its field $\\m athbb{F}\, (\\mathbb{F}\\in\\{\\mathbb{R}\,\\mathbb{C} \\})$. The approxim ation is similar to the well known universal approximation theorems for co ntinuous functions from $\\mathbb{R}^n$ to $\\mathbb{R}$ with (multilayer) neural networks by Cybenko\, Hornik et al.\, Funahashi\, Leshno et al. Si milar to classical neural networks\, the approximating function is easy to implement and allows for fast computation and fitting. Few applications g eared toward derivative pricing and numerical solutions of parabolic parti al differential equations will be outlined.\n\nReferences:\n\nG. Cybenko. Approximation by superpositions of a sigmoidal function. Mathematics of Co ntrol\, Signals and Systems\, 2(4):303–314\, 1989.\n\nK. Hornik\, M. Sti nchcombe\, and H. White. Multilayer feedforward networks are universal app roximators. Neural Networks\, 2(5):359–366\, 1989. \n\nK.-I. Funahashi. On the approximate realization of continuous mappings by neural networks. NeuralNetworks\, 2(3):183–192\, 1989. \n\nM. Leshno\, V. Y. Lin\, A. Pin kus\, and S. Schocken. Multilayer feedforward networks with a nonpolynomia l activation function can approximate any function. Neural Networks\, 6(6) :861–867\, 1993.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Asma Khedher (University of Amsterdam) DTSTART:20211105T090000Z DTEND:20211105T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/28 DESCRIPTION:Title: An infinite-dimensional affine stochastic volatility model\nby Asma Khedher (University of Amsterdam) as part of STAR seminars\n\n \nAbstract\nWe introduce a flexible and tractable infinite-dimensional sto chastic volatility model. More specifically\, we consider a Hilbert space valued Ornstein–Uhlenbeck-type process\, whose instantaneous covariance is given by a pure-jump stochastic process taking values in the cone of po sitive self-adjoint Hilbert-Schmidt operators. The tractability of our mod el lies in the fact that the two processes involved are jointly affine\, i .e.\, we show that their characteristic function can be given explicitly i n terms of the solutions to a set of generalised Riccati equations. The fl exibility lies in the fact that we allow multiple modeling options for the instantaneous covariance process\, including state-dependent jump intensi ty.\nInfinite dimensional volatility models arise e.g. when considering th e dynamics of forward rate functions in the Heath-Jarrow-Morton-Musiela mo deling framework using the Filipović space. In this setting we discuss va rious examples: an infinite-dimensional version of the Barndorff-Nielsen –Shephard stochastic volatility model\, as well as a model involving sel f-exciting volatility.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Michèle Vanmaele (University of Ghent) DTSTART:20211105T100000Z DTEND:20211105T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/29 DESCRIPTION:Title: Mortality/Longevity Risk-Minimization with or without Securi tization\nby Michèle Vanmaele (University of Ghent) as part of STAR s eminars\n\n\nAbstract\nIn this talk we will address the risk-minimization problem\, with and without mortality securitization\,\nà la Föllmer–So ndermann for a large class of equity-linked mortality contracts when no\nm odel for the death time is specified. This framework includes situations i n which the correlation\nbetween the market model and the time of death is arbitrary general\, and hence leads to the case of a\nmarket model where there are two levels of information—the public information\, which is ge nerated\nby the financial assets\, and a larger flow of information that c ontains additional knowledge about\nthe death time of an insured. We will derive the dynamics of the value processes of the mortality/longevity secu rities used for the securitization\, and decompose any mortality/longevity liability into the sum of orthogonal risks by means of a risk basis. Next \, we will quantify\, as explicitly as possible\, the effect of mortality on the risk-minimizing strategy by determining the optimal strategy in the enlarged filtration in terms of strategies in the smaller filtration. We will obtain \n risk-minimizing strategies with insurance securitization by investing in stocks and one (or more) mortality/longevity derivatives suc h as longevity bonds. \n\nThe talk is based on joint work with Tahir Choul l (University of Alberta)i and Catherine Daveloose (Ghent University).\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Julian Tugaut (Université Jean Monnet\, Saint-Etienne) DTSTART:20211109T121500Z DTEND:20211109T130000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/30 DESCRIPTION:by Julian Tugaut (Université Jean Monnet\, Saint-Etienne) as part of STAR seminars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/30/ END:VEVENT BEGIN:VEVENT SUMMARY:1-day workshop (Multiple) DTSTART:20211112T080000Z DTEND:20211112T160000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/31 DESCRIPTION:Title: Recent Developments in Stochastics 2021\nby 1-day worksh op (Multiple) as part of STAR seminars\n\n\nAbstract\nThe STAR research se minar is replaced today by the 1.day workshop\nRecent Developments in Stoc hastics 2021\nFor information\, please visit\nhttps://www.mn.uio.no/math/e nglish/research/projects/storm/events/conferences/recent-developments-in-s tochastics%281%29/index.html\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Carlo Sgarra (Politecnico di Milano) DTSTART:20211210T090000Z DTEND:20211210T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/32 DESCRIPTION:Title: Optimal Reinsurance Strategies in a Partially Observable Con tagion Model\nby Carlo Sgarra (Politecnico di Milano) as part of STAR seminars\n\n\nAbstract\nWe investigate the optimal reinsurance problem whe n the loss process exhibits jump clustering features and the insurance com pany has restricted information about the loss process. We maximize expect ed exponential utility and show that an optimal solution exists. We provid e the equation governing the dynamics of the (infinite-dimensional) filter and characterize the solution of the stochastic optimization problem as t he solution of a BSDE.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/32/ END:VEVENT BEGIN:VEVENT SUMMARY:2-days workshop (Multiple) DTSTART:20211125T070000Z DTEND:20211125T140000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/33 DESCRIPTION:Title: Rough path techniques in stochastic analysis and mathematica l probability\nby 2-days workshop (Multiple) as part of STAR seminars\ n\nAbstract: TBA\n\nPlease visit the dedicated webpage:\nhttps://www.mn.ui o.no/math/english/research/projects/storm/events/conferences/rough-path-te chniques-in-stochastic-analysis-and-m/rough-path-techniques-in-stochastic- analysis-and-m.html\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/33/ END:VEVENT BEGIN:VEVENT SUMMARY:2-days workshop (Multiple) DTSTART:20211126T070000Z DTEND:20211126T140000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/34 DESCRIPTION:Title: Rough path techniques in stochastic analysis and mathematica l probability\nby 2-days workshop (Multiple) as part of STAR seminars\ n\n\nAbstract\nPlease visit the dedicated webpage:\nhttps://sites.google.c om/view/rpisa2021/start\n\nhttps://www.mn.uio.no/math/english/research/pro jects/storm/events/conferences/rough-path-techniques-in-stochastic-analysi s-and-m/rough-path-techniques-in-stochastic-analysis-and-m.html\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Sven Karbach (University of Amsterdam) DTSTART:20211210T100000Z DTEND:20211210T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/35 DESCRIPTION:Title: Positive multivariate CARMA processe\nby Sven Karbach (U niversity of Amsterdam) as part of STAR seminars\n\n\nAbstract\nIn this ta lk we discuss positivity of multivariate continuous-time autoregressive mo ving-average (MCARMA) processes. In particular\, we introduce matrix value d MCARMA processes and derive sufficient and necessary conditions such tha t the processes leave the cone of positive semi-definite matrices invarian t. MCARMA processes on the cone of positive semi-definite matrices can be used to model e.g. the instantaneous covariance process in multivariate st ochastic volatility models.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Lord (Radbrukne University) DTSTART:20220121T100000Z DTEND:20220121T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/36 DESCRIPTION:Title: GBM based exponential integrators\nby Gabriel Lord (Radb rukne University) as part of STAR seminars\n\n\nAbstract\nWe introduce a t ype of exponential time integrator which exploits linear terms in both the drift and diffusion for Stochastic Differential Equations (SDEs). We deri ve the scheme and show how it can be extended to general SDEs and discuss strong convergence. We initially examine strong convergence for globally L ipschitz drift and diffusion before introducing a tamed version. We illust rate the efficiency by considering some well-known SDE models. If time pe rmits I will discuss weak convergence of these schemes.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Yaozhong Hu (University of Alberta) DTSTART:20220204T100000Z DTEND:20220204T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/37 DESCRIPTION:Title: Parameter estimation for threshold Ornstein-Uhlenbeck proces ses from discrete observations\nby Yaozhong Hu (University of Alberta) as part of STAR seminars\n\n\nAbstract\nAssuming that a threshold Ornstei n-Uhlenbeck process is observed at discrete time instants\, we shall prese nt the generalized moment estimators to estimate the parameters. The the oretical basis is the celebrated ergodic theorem. To use this theorem we n eed to find the explicit form of the invariant measure. With the sampling time step arbitrarily fixed\, we prove the strong consistency and asymptot ic normality of our estimators as the sample size tends to infinity.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Colin Ramsay (University of Nebraska-Lincoln) DTSTART:20220218T100000Z DTEND:20220218T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/38 DESCRIPTION:Title: CANCELLED - Doubly Enhanced Medicaid Partnership Annuities ( DEMPANs): A New Tool for Providing Long Term Care to Retired U.S. Seniors in the Medicaid Penumbra\nby Colin Ramsay (University of Nebraska-Linc oln) as part of STAR seminars\n\n\nAbstract\nCANCELLED - NEW DATE WILL BE ANNOUNCED IN DUE TIME\n\n\nA major problem facing many U.S. retirees is ac cessing and paying for long term care. The 2019 National Association of In surance Commissioners (NAIC) guide on long term care insurance estimates t hat\, of the individuals living in the U.S. who reach age 65\, about 70% a re expected to need some form of long term care at least once in their lif etime and about 35% are expected to enter a nursing home at least once in their lifetime. Although Medicare covers most of a U.S. retiree’s medica l care\, Medicare does not ordinarily pay for long term care. U.S. retiree s often can access long term care services via the Medicaid program\, whic h is a means-tested program geared to lower income Americans. But\, to qui ckly qualify for Medicaid\, many retirees take drastic steps such as trans ferring their assets to family members. When access to long term care is n ot urgent and long term planning is an option\, most U.S. States have deve loped so-called Partnership for Long Term Care (PLTC) Program insurance po licies that provide access to Medicaid services while sheltering some or a ll of a retiree’s assets. In this paper\, we pro11 pose a hybrid annuity product called a doubly enhanced Medicaid Partnership annuity (DEMPAN) th at combines an annuity with a long term care rider that is integrated with in the framework of a qualified Partnership policy. (Outside the U.S.\, bu ndled retirement products similar to DEMPANs are called life-care annuitie s.) To analyze our DEMPANs\, we use a multi-state model of long term care with health states that are based on a retiree’s ability to perform acti vities of daily living (ADLs)\, instrumental activities of daily living (I ADLs)\, and cognitive ability. A significant contribution of this paper is to explicitly model how the quality of long term care a retiree receives affects the retiree’s health state transition probabilities used in the multi-state model. As higher quality of care usually comes at a higher cos t but with better health outcomes\, we provided an example that explores a n expected discounted utility maximizing retiree’s optimal choice of DEM PAN. Our example showed that it may be optimal for retirees who purchase D EMPANs to buy average quality long term care. We hope DEMPANs fill a gap i n the long term care market by providing an important tool for eldercare p lanning for those in the Medicaid penumbra (i.e.\, in the middle and lower -middle income classes). Retirees who purchase DEMPANs have the benefits o f an annuity\, private long term care\, Medicaid assistance with paying th eir long term care bills\, and some degree of asset protection from Medica id estate recovery.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Nils Detering (UC Santa Barbara) DTSTART:20220304T100000Z DTEND:20220304T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/39 DESCRIPTION:Title: When do you Stop Supporting your Bankrupt Subsidiary\nby Nils Detering (UC Santa Barbara) as part of STAR seminars\n\n\nAbstract\n We consider a network of bank holdings\, where every holding has two subsi diaries of different type. A subsidiary can trade with another holding's s ubsidiary of the same type. Holdings support their subsidiary up to a cert ain level when they would otherwise fail to honor their financial obligati ons. We investigate the spread of contagion in this banking network when t he number of bank holdings is large\, and find the final number of default ed subsidiaries under different rules for the holding support. We also con sider resilience of this multilayered network to small shocks. Our work sh eds light onto the role that holding structures can play in the amplificat ion of financial stress. \nWe find that depending on the capitalisation o f the network\, a holding structure can be beneficial as compared to small er separated entities. In other instances it can be harmful and actually i ncrease contagion.\nWe illustrate our results in a numerical case study an d also determine the optimal level of holding support from a regulator per spective.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Emanuela Rosazza Gianin (University of Milano Bicocca) DTSTART:20220318T100000Z DTEND:20220318T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/40 DESCRIPTION:Title: Generalized PELVE and applications to risk measures\nby Emanuela Rosazza Gianin (University of Milano Bicocca) as part of STAR sem inars\n\n\nAbstract\nThe continuing evolution of insurance and banking reg ulation has\nraised interest in the calibration of different risk measures associated\nwith suitable confidence levels. In particular\, Li and Wang (2019)\nhave introduced a probability equivalent level (called PELVE) for the\nreplacement of Value at Risk with Conditional Value at Risk. \nIn thi s talk\, we propose two alternative generalizations of PELVE (distorted PE LVE and generalized PELVE) by means of distortion functions in the former case\, while to more general pairs of risk measures in the latter. Condit ions for the existence\nand uniqueness of distorted and generalized PELVE and additional properties for specific families of risk measures are discu ssed. \nA study of Generalized Pareto Distributions reveals\nan interestin g correspondence between PELVE and generalized PELVE\, and explores\ntheir relationship with the tail index. An empirical application\nillustrates t he usefulness of (generalized) PELVE in characterizing tail behavior\nnot only for individual asset returns\, but also for possible portfolio\ncombi nations.\nBased on a joint work with Anna Maria Fiori.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Erlend Grong (University of Bergen) DTSTART:20220401T090000Z DTEND:20220401T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/41 DESCRIPTION:Title: Path space on sub-Riemannian manifolds\nby Erlend Grong (University of Bergen) as part of STAR seminars\n\n\nAbstract\nWe discuss how we can generalize the concept of Malliavin Calculus to the setting of a sub-Riemannian manifolds. We explain how concepts such as the Cameron-Ma rtin space\, the gradient and damped gradient of functions on path space c an be understood in this setting. As an application\, we show how we can o btain functional inequalities related to both a lower and upper bounds for Ricci curvature. These results are from a joint work with Li-Juan Cheng a nd Anton Thalmaier.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/41/ END:VEVENT BEGIN:VEVENT SUMMARY:José Garrido (Concordia University Montreal) DTSTART:20220427T101500Z DTEND:20220427T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/42 DESCRIPTION:Title: Bridging epidemiological and actuarial models: the case of C OVID-19\nby José Garrido (Concordia University Montreal) as part of S TAR seminars\n\n\nAbstract\nOur society's efforts to fight pandemics rely heavily on our ability to understand\, model and predict the transmission dynamics of infectious diseases. Compartmental models are among the most c ommonly used mathematical tools to explain reported infections and deaths. This collective book chapter offers a brief overview of basic compartment al models as well as several actuarial applications\, ranging from product design and reserving of epidemic insurance\, to the projection of healthc are demand and the allocation of scarce resources. The intent is to bridge classical epidemiological models with actuarial and financial application s that provide healthcare coverage and utilise limited healthcare resource s during pandemics.\n\nAuthors: R. Feng (University of Illinois at Urbana- -Champaign\, UIUC)\, J. Garrido (Concordia University)\, L. Jin\, L. Zhang (UIUC) and S-H. Loke (Central Washington University)\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Eduardo Abi Jaber (Université Paris 1 Panthéon-Sorbonne) DTSTART:20220506T090000Z DTEND:20220506T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/43 DESCRIPTION:Title: Quadratic Gaussian models: analytic expressions for pricing and portfolio allocation\nby Eduardo Abi Jaber (Université Paris 1 Pa nthéon-Sorbonne) as part of STAR seminars\n\n\nAbstract\nStochastic model s based on Gaussian processes\, like fractional Brownian motion\, are able to reproduce important stylized facts of financial markets such as rich a utocorrelation structures\, persistence and roughness of sample paths. Thi s is made possible by virtue of the flexibility introduced in the choice o f the covariance function of the Gaussian process. The price to pay is tha t\, in general\, such models are no longer Markovian nor semimartingales\, which limits their practical use. We derive explicit analytic expressions for Fourier-Laplace transforms of quadratic functionals of Gaussian proce sses. Such analytic expression can be approximated by closed form matrix e xpressions stemming from Wishart distributions. \nWe highlight the applica bility of such result in the context of rough volatility modeling: (i) fa st pricing and calibration in the (rough) fractional Stein-Stein model\; ( ii) explicit solutions for the Markowitz portfolio allocation problem in a multivariate rough Stein—Stein model.\nBased on joint works with Enzo M iller and Huyên Pham.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Olena Tymoshenko (Kiev Polytechnique Institute) DTSTART:20220520T080000Z DTEND:20220520T090000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/44 DESCRIPTION:by Olena Tymoshenko (Kiev Polytechnique Institute) as part of STAR seminars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Kjetil Røysland (University of Oslo) DTSTART:20220520T090000Z DTEND:20220520T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/45 DESCRIPTION:by Kjetil Røysland (University of Oslo) as part of STAR semin ars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Riedle (Kings College London) DTSTART:20220603T080000Z DTEND:20220603T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/46 DESCRIPTION:Title: Minicourse: Introduction to Cylindrical Lévy processes Part I\nby Markus Riedle (Kings College London) as part of STAR seminars\n \n\nAbstract\nCylindrical Lévy processes are a natural extension of cylin drical Brownian motion which has been the standard model of random perturb ations of partial differential equations and other models in infinite dime nsions for the last 50 years. Here\, the attribute cylindrical refers to t he fact that cylindrical Brownian motions are not classical stochastic pro cesses attaining values in the underlying space but are generalised object s. The reasons for the choice of cylindrical but not classical Brownian mo tion can be found in the facts that there does not exist a classical Brown ian motion with independent components in an infinite dimensional Hilbert space\, and that cylindrical processes enable a very flexible modelling of random noise in time and space.\nIn this lecture series\, we briefly pres ent some aspects of the theory of cylindrical measures and cylindrical ran dom variables. We introduce cylindrical Lévy processes and present some s pecific examples in detail and discuss their relations to other models of random perturbations in the literature. We present a theory of stochastic integration with respect to cylindrical random variables\, which cannot re ly on the classical approach\, as cylindrical Lévy processes do not enjoy a semi-martingale decomposition. We finish this lecture series by investi gating some specific models driven by cylindrical Lévy processes\, such a s Ornstein-Uhlenbeck processes.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Riedle (Kings College London) DTSTART:20220614T090000Z DTEND:20220614T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/47 DESCRIPTION:Title: Minicourse: Introduction to Cylindrical Lévy processes Part II\nby Markus Riedle (Kings College London) as part of STAR seminars\ n\n\nAbstract\nCylindrical Lévy processes are a natural extension of cyli ndrical Brownian motion which has been the standard model of random pertur bations of partial differential equations and other models in infinite dim ensions for the last 50 years. Here\, the attribute cylindrical refers to the fact that cylindrical Brownian motions are not classical stochastic pr ocesses attaining values in the underlying space but are generalised objec ts. The reasons for the choice of cylindrical but not classical Brownian m otion can be found in the facts that there does not exist a classical Brow nian motion with independent components in an infinite dimensional Hilbert space\, and that cylindrical processes enable a very flexible modelling o f random noise in time and space.\nIn this lecture series\, we briefly pre sent some aspects of the theory of cylindrical measures and cylindrical ra ndom variables. We introduce cylindrical Lévy processes and present some specific examples in detail and discuss their relations to other models of random perturbations in the literature. We present a theory of stochastic integration with respect to cylindrical random variables\, which cannot r ely on the classical approach\, as cylindrical Lévy processes do not enjo y a semi-martingale decomposition. We finish this lecture series by invest igating some specific models driven by cylindrical Lévy processes\, such as Ornstein-Uhlenbeck processes.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Riedle (Kings College London) DTSTART:20220617T080000Z DTEND:20220617T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/48 DESCRIPTION:Title: Minicourse: Introduction to Cylindrical Lévy processes Part III\nby Markus Riedle (Kings College London) as part of STAR seminars \n\n\nAbstract\nCylindrical Lévy processes are a natural extension of cyl indrical Brownian motion which has been the standard model of random pertu rbations of partial differential equations and other models in infinite di mensions for the last 50 years. Here\, the attribute cylindrical refers to the fact that cylindrical Brownian motions are not classical stochastic p rocesses attaining values in the underlying space but are generalised obje cts. The reasons for the choice of cylindrical but not classical Brownian motion can be found in the facts that there does not exist a classical Bro wnian motion with independent components in an infinite dimensional Hilber t space\, and that cylindrical processes enable a very flexible modelling of random noise in time and space.\nIn this lecture series\, we briefly pr esent some aspects of the theory of cylindrical measures and cylindrical r andom variables. We introduce cylindrical Lévy processes and present some specific examples in detail and discuss their relations to other models o f random perturbations in the literature. We present a theory of stochasti c integration with respect to cylindrical random variables\, which cannot rely on the classical approach\, as cylindrical Lévy processes do not enj oy a semi-martingale decomposition. We finish this lecture series by inves tigating some specific models driven by cylindrical Lévy processes\, such as Ornstein-Uhlenbeck processes.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Péter Vékás (Corvinus University of Budapest) DTSTART:20220923T090000Z DTEND:20220923T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/49 DESCRIPTION:Title: AI in Longevity Risk Management: Improved Long-Term Projecti ons by Machine Learning\nby Péter Vékás (Corvinus University of Bud apest) as part of STAR seminars\n\n\nAbstract\nWhile human mortality has d ecreased significantly since the beginning of the past century\, resulting in unprecedented increases in human life expectancies\, several authors h ave noted a historical pattern of diminishing mortality decline at relativ ely younger ages along with accelerating improvements among the elderly. L i\, Lee and Gerland (2013) call this phenomenon the ’rotation’ of the age pattern of mortality decline. A somewhat simplistic explanation of thi s is that spectacular decreases in infant and childhood mortality rates (e .g.\, due to widespread vaccination programs and improved child nutrition) are less and less possible\, while costly medical procedures to extend li fe at advanced ages are increasingly available.\nThe practical actuarial s ignificance of the topic is that ignoring rotation in long-term mortality forecasts may lead to a severe and systematic underestimation of the old-a ged population\, which exacerbates longevity risk and may lead to serious adverse financial consequences for life and health insurers as well as pen sion schemes.\nThe popular model of Lee and Carter (1992) as well as many other mortality forecasting techniques do not allow for rotation at all. T o correct this shortcoming\, Li\, Lee and Gerland (2013) introduced a vari ant of the Lee–Carter model including rotation. This model extension ass umes that the evolution of mortality improvement rates follows a parametri c equation\, whose two parameters govern the speed of rotation and the lev el of life expectancy where the process begins.\nWe use age-specific morta lity rates of all countries by gender from the Human Mortality Database (H MD)\, and split the available time periods by country into a training set spanning from the first available year up to 1990\, a validation set from 1991 to 1999 and a test set containing all years after 1999. Instead of fi xed values of the two parameters mentioned in the previous paragraph\, as suggested by Li\, Lee and Gerland (2013)\, we propose to treat them as hyp erparameters and optimize them on the validation set\, as it is customaril y done in machine learning\, in order to improve long- term forecasting pe rformance. Additionally\, we propose deep neural networks specifically des igned to capture the rotation of mortality decline in order to produce eve n more data-driven rotation schedules free of any prior assumptions\, and we tune the hyperparameters of the networks on the validation set. As a th ird candidate\, we also propose a generalized additive model involving the bivariate spline approximation of the residuals of the Lee–Carter model . This approach is halfway between fully parametric models such as the var iant of the Lee–Carter model including rotation and fully data-driven on es such as deep neural networks.\nWe use the test set to assess and compar e the performance of the rotated variant of the Lee–Carter model includi ng hyperparameter tuning\, the deep neural network capturing rotation and the spline GAM approach. We will point out which approach works best in th e long run in every country\, which countries are more or less prone to ro tation\, and how actual rotation schedules differ from the parametric form hypothesized by Li\, Lee and Gerland (2013).\nFinally\, we use our models to assess longevity risk in a pension scheme and point out the potential financial benefits of implementing our improved methods of capturing rotat ion in mortality data\, and also elaborate on the potential impact of COVI D-19 and how it is best incorporated into these models.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Knut Sølna (University of California\, Irvine) DTSTART:20221028T090000Z DTEND:20221028T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/50 DESCRIPTION:Title: Asymptotics with Rough and Multiscale Stochastic Volatility< /a>\nby Knut Sølna (University of California\, Irvine) as part of STAR se minars\n\n\nAbstract\nWe discuss some stochastic volatility models used in mathematical finance. The stochastic volatility modeling involves multisc ale frameworks and the asymptotic analysis of the associated stochastic di fferential equations exploits separation of time scales. The asymptotic an alysis leads to parsimonious expressions for pricing of various financial instruments. Recent empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset and we p resent in particular results for so-called rough volatility models motivat ed by such observations.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Tomasz Klimsiak (Nicolaus Copernicus University) DTSTART:20221129T100000Z DTEND:20221129T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/51 DESCRIPTION:Title: Non-semimartingale solutions to reflected BSDEs with applica tions to Dynkin games\nby Tomasz Klimsiak (Nicolaus Copernicus Univers ity) as part of STAR seminars\n\n\nAbstract\nt is well known that the theo ry of Reflected BSDEs is well-posed under the Mokobodzki condition on the barriers L\,U. This is due to the fact that by the very definition of a so lution to RBSDE\, its first component is a semimartingale that lies betwee n the barriers - this is exactly the content of the (weak) Mokobodzki cond ition. However\, there is an intimate connection between solutions of RBSD Es and value processes in Dynkin games and it is well known that in some i nstances the latter process is well defined even if Mokobodzki’s conditi on does not hold\, so the natural question arises whether such a process s olves in a unique way certain backward SDE. Our goal is to extend the noti on of RBSDEs and provide the existence and uniqueness results to obtain a one-to-one correspondence between solutions of RBSDEs and value processes in nonlinear Dynkin games.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Saul Jacka (University of Warwick) DTSTART:20221214T100000Z DTEND:20221214T110000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/52 DESCRIPTION:Title: CANCELLED - Optimal Stopping and Technical Analysis\nby Saul Jacka (University of Warwick) as part of STAR seminars\n\n\nAbstract\ nThe seminar is cancelled and postponed. New date will be announced.\n\nAb stract:\nTechnical Analysis is a collection of investment policies based o n the history of price processes. It is widely used by institutional inves tors despite conflict with the Efficient Markets Hypothesis. In this talk we'll discuss a very general model of a stock price which is designed to a nalyse the viability of a form of technical analysis known as the support and resistance line method.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Frank Riedel (University of Bielefeld) DTSTART:20230315T121500Z DTEND:20230315T130000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/53 DESCRIPTION:Title: Approaches to Knightian Uncertainty in Finance and Economics \nby Frank Riedel (University of Bielefeld) as part of STAR seminars\n \n\nAbstract\nThe lecture reviews recent model of preferences under Knigh tian uncertainty. These approaches are closely related to attempts to quan tify risk in finance. A particular focus will be on the so-called smooth m odel\, an ambiguity-averse version of a second-order Bayesian Ansatz\, th at goes back to Klibanoff\, Marinacci\, and Mukerji (Econometrica 2005). W e will study its axiomatic foundations and discuss the relationship of th is approach with statistics\, in particular the issue of identification of models (Denti\, Pomatto\, Econometrica 2022). Moreover\, we show how the smooth model is related to variational and coherent risk measures. The le cture will provide the necessary background for the lecture on Friday.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Frank Riedel (University of Bielefeld) DTSTART:20230317T091500Z DTEND:20230317T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/54 DESCRIPTION:Title: Efficient Allocations under Ambiguous Model Uncertainty\ nby Frank Riedel (University of Bielefeld) as part of STAR seminars\n\n\nA bstract\nWe investigate consequences of model uncertainty (or ambiguity) o n ex ante efficient allocations in an exchange economy. The ambiguity we c onsider is embodied in the model uncertainty perceived by the decision mak er: they are unsure what would be the appropriate probability measure to a pply to evaluate contingent consumption contingent plans and keep in cons ideration a set of alternative probabilistic laws. We study the case whe re the typical consumer in the economy is ambiguity-averse with smooth amb iguity preferences and the set of priors P is point identified\, i.e.\, t he true law p can be recovered empirically from observed events. Different ly from the literature\, we allow for the case where the aggregate risk is ambiguous and agents are heterogeneously ambiguity averse. Our analysis a ddresses\, in particular\, the full range of set-ups where under expected utility the Pareto efficient consumption sharing rule is a linear function of the aggregate endowment. We identify systematic differences ambiguity aversion introduces to optimal sharing arrangements in these environments and also characterize the representative consumer. Furthermore\, we invest igate the implications for the state-price function\, in particular\, the effect of heterogeneity in ambiguity aversion.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Dennis Schroers (University of Bonn) DTSTART:20230421T090000Z DTEND:20230421T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/55 DESCRIPTION:by Dennis Schroers (University of Bonn) as part of STAR semina rs\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Emanuela Rosazza-Gianin (University Bicocca-Milano) DTSTART:20230421T080000Z DTEND:20230421T090000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/56 DESCRIPTION:by Emanuela Rosazza-Gianin (University Bicocca-Milano) as part of STAR seminars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Andreas Petersson (University of Oslo) DTSTART:20230428T090000Z DTEND:20230428T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/57 DESCRIPTION:by Andreas Petersson (University of Oslo) as part of STAR semi nars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Christa Cuchiero (University of Vienna) DTSTART:20230329T110000Z DTEND:20230329T140000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/58 DESCRIPTION:Title: Signature methods in finance I\nby Christa Cuchiero (Uni versity of Vienna) as part of STAR seminars\n\n\nAbstract\nSignature metho ds represent a non-parametric way for extracting characteristic features f rom time series data which is essential in machine learning tasks. This ex plains why these techniques become more and more popular in Econometrics a nd Mathematical Finance. Indeed\, signature based approaches allow for dat a-driven and thus more robust model selection mechanisms\, while first pri nciples like no arbitrage can still be easily guaranteed. \n\nIn this cour se we shall focus on the use of signature as universal linear regression b asis of continuous functionals of paths for financial applications. \nWe f irst give an introduction to continuous rough paths and show how to embed continuous semimartingales into the rough path setting. Indeed our main fo cus lies on signature of semimartingales\, one of the main modeling tools in finance. By relying on the Stone-Weierstrass theorem we show how to pro ve the universal approximation property of linear functions of the signatu re in appropriate topologies on path space. To cover models with jumps we shall additionally introduce the notion of cadlag rough paths\, Marcus sig nature and its universal approximation properties in appropriate Skorokhod topologies. \n\nIn the financial applications that we have in mind one ke y quantity that one needs to compute is the expected signature of some und erlying process. Surprisingly this can be achieved for generic classes of jump diffusions (with possibly path dependent characteristics) via techniq ues from affine and polynomial processes. More precisely\, we show how the signature process of these jump diffusions can be embedded in the framewo rk of affine and polynomial processes. These classes of processes have bee n -- due to their tractability -- the dominating process class prior to th e new era of highly over-parametrized dynamic models. Following this line we obtain that the infinite dimensional Feynman Kac PIDE of the signature process can generically be reduced to an infinite dimensional ODE either of Riccati or linear type. This then allows to get power series expansions for the expected signature and the Fourier-Laplace transform. \n\nIn term s of financial applications\, we shall treat two main topics: stochastic p ortfolio theory and signature based asset price models. \n\nIn the context of stochastic portfolio theory we introduce a novel class of portfolios w hich we call linear path-functional portfolios. These are portfolios which are determined by certain transformations of linear functions of a collec tions of feature maps that are non-anticipative path functionals of an und erlying semimartingale. As main example for such feature maps we consider signature of the (ranked) market weights. Relying on the universal approxi mation theorem we show that every continuous (possibly path-dependent) po rtfolio function of the market weights can be uniformly approximated by si gnature portfolios. Besides these universality features\, the main numeric al advantage lies in the fact that several optimization tasks like maximiz ing expected logarithmic utility or mean-variance optimization within the class of linear path-functional portfolios reduces to a convex quadratic o ptimization problem\, thus making it computationally highly tractable. We apply our method to real market data and show generic out-performance on o ut-of-sample data even under transaction costs. \n\nIn view of asset price models we consider a stochastic volatility model where the dynamics of th e volatility are described by linear functions of the (time extended) sign ature of a primary underlying process\, which is supposed to be some multi dimensional continuous semimartingale. Under the additional assumption tha t this primary process is of polynomial type\, we obtain closed form expre ssions for the VIX squared\, exploiting the fact that the truncated signat ure of a polynomial process is again a polynomial process. Adding to such a primary process the Brownian motion driving the stock price\, allows the n to express both the log-price and the VIX squared as linear functions of the signature of the corresponding augmented process. This feature can th en be efficiently used for pricing and calibration purposes. Indeed\, as the signature samples can be easily precomputed\, the calibration task can be split into an offline sampling and a standard optimization. For both the SPX and VIX options we obtain highly accurate calibration results\, sh owing that this model class allows to solve the joint calibration problem without adding jumps or rough volatility.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Christa Cuchiero (University of Vienna) DTSTART:20230331T080000Z DTEND:20230331T100000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/59 DESCRIPTION:Title: Signature methods in finance III\nby Christa Cuchiero (U niversity of Vienna) as part of STAR seminars\n\n\nAbstract\nSignature met hods represent a non-parametric way for extracting characteristic features from time series data which is essential in machine learning tasks. This explains why these techniques become more and more popular in Econometrics and Mathematical Finance. Indeed\, signature based approaches allow for d ata-driven and thus more robust model selection mechanisms\, while first p rinciples like no arbitrage can still be easily guaranteed. \n\nIn this co urse we shall focus on the use of signature as universal linear regression basis of continuous functionals of paths for financial applications. \nWe first give an introduction to continuous rough paths and show how to embe d continuous semimartingales into the rough path setting. Indeed our main focus lies on signature of semimartingales\, one of the main modeling tool s in finance. By relying on the Stone-Weierstrass theorem we show how to p rove the universal approximation property of linear functions of the signa ture in appropriate topologies on path space. To cover models with jumps w e shall additionally introduce the notion of cadlag rough paths\, Marcus s ignature and its universal approximation properties in appropriate Skorokh od topologies. \n\nIn the financial applications that we have in mind one key quantity that one needs to compute is the expected signature of some u nderlying process. Surprisingly this can be achieved for generic classes o f jump diffusions (with possibly path dependent characteristics) via techn iques from affine and polynomial processes. More precisely\, we show how t he signature process of these jump diffusions can be embedded in the frame work of affine and polynomial processes. These classes of processes have b een -- due to their tractability -- the dominating process class prior to the new era of highly over-parametrized dynamic models. Following this lin e we obtain that the infinite dimensional Feynman Kac PIDE of the signatur e process can generically be reduced to an infinite dimensional ODE eithe r of Riccati or linear type. This then allows to get power series expansio ns for the expected signature and the Fourier-Laplace transform. \n\nIn te rms of financial applications\, we shall treat two main topics: stochastic portfolio theory and signature based asset price models. \n\nIn the conte xt of stochastic portfolio theory we introduce a novel class of portfolios which we call linear path-functional portfolios. These are portfolios whi ch are determined by certain transformations of linear functions of a coll ections of feature maps that are non-anticipative path functionals of an u nderlying semimartingale. As main example for such feature maps we conside r signature of the (ranked) market weights. Relying on the universal appro ximation theorem we show that every continuous (possibly path-dependent) portfolio function of the market weights can be uniformly approximated by signature portfolios. Besides these universality features\, the main numer ical advantage lies in the fact that several optimization tasks like maxim izing expected logarithmic utility or mean-variance optimization within th e class of linear path-functional portfolios reduces to a convex quadratic optimization problem\, thus making it computationally highly tractable. W e apply our method to real market data and show generic out-performance on out-of-sample data even under transaction costs. \n\nIn view of asset pri ce models we consider a stochastic volatility model where the dynamics of the volatility are described by linear functions of the (time extended) si gnature of a primary underlying process\, which is supposed to be some mul tidimensional continuous semimartingale. Under the additional assumption t hat this primary process is of polynomial type\, we obtain closed form exp ressions for the VIX squared\, exploiting the fact that the truncated sign ature of a polynomial process is again a polynomial process. Adding to suc h a primary process the Brownian motion driving the stock price\, allows t hen to express both the log-price and the VIX squared as linear functions of the signature of the corresponding augmented process. This feature can then be efficiently used for pricing and calibration purposes. Indeed\, a s the signature samples can be easily precomputed\, the calibration task c an be split into an offline sampling and a standard optimization. For bot h the SPX and VIX options we obtain highly accurate calibration results\, showing that this model class allows to solve the joint calibration proble m without adding jumps or rough volatility.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Christa Cuchiero (University of Vienna) DTSTART:20230330T110000Z DTEND:20230330T140000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/60 DESCRIPTION:Title: Signature methods in finance II\nby Christa Cuchiero (Un iversity of Vienna) as part of STAR seminars\n\n\nAbstract\nSignature meth ods represent a non-parametric way for extracting characteristic features from time series data which is essential in machine learning tasks. This e xplains why these techniques become more and more popular in Econometrics and Mathematical Finance. Indeed\, signature based approaches allow for da ta-driven and thus more robust model selection mechanisms\, while first pr inciples like no arbitrage can still be easily guaranteed. \n\nIn this cou rse we shall focus on the use of signature as universal linear regression basis of continuous functionals of paths for financial applications. \nWe first give an introduction to continuous rough paths and show how to embed continuous semimartingales into the rough path setting. Indeed our main f ocus lies on signature of semimartingales\, one of the main modeling tools in finance. By relying on the Stone-Weierstrass theorem we show how to pr ove the universal approximation property of linear functions of the signat ure in appropriate topologies on path space. To cover models with jumps we shall additionally introduce the notion of cadlag rough paths\, Marcus si gnature and its universal approximation properties in appropriate Skorokho d topologies. \n\nIn the financial applications that we have in mind one k ey quantity that one needs to compute is the expected signature of some un derlying process. Surprisingly this can be achieved for generic classes of jump diffusions (with possibly path dependent characteristics) via techni ques from affine and polynomial processes. More precisely\, we show how th e signature process of these jump diffusions can be embedded in the framew ork of affine and polynomial processes. These classes of processes have be en -- due to their tractability -- the dominating process class prior to t he new era of highly over-parametrized dynamic models. Following this line we obtain that the infinite dimensional Feynman Kac PIDE of the signature process can generically be reduced to an infinite dimensional ODE either of Riccati or linear type. This then allows to get power series expansion s for the expected signature and the Fourier-Laplace transform. \n\nIn ter ms of financial applications\, we shall treat two main topics: stochastic portfolio theory and signature based asset price models. \n\nIn the contex t of stochastic portfolio theory we introduce a novel class of portfolios which we call linear path-functional portfolios. These are portfolios whic h are determined by certain transformations of linear functions of a colle ctions of feature maps that are non-anticipative path functionals of an un derlying semimartingale. As main example for such feature maps we consider signature of the (ranked) market weights. Relying on the universal approx imation theorem we show that every continuous (possibly path-dependent) p ortfolio function of the market weights can be uniformly approximated by s ignature portfolios. Besides these universality features\, the main numeri cal advantage lies in the fact that several optimization tasks like maximi zing expected logarithmic utility or mean-variance optimization within the class of linear path-functional portfolios reduces to a convex quadratic optimization problem\, thus making it computationally highly tractable. We apply our method to real market data and show generic out-performance on out-of-sample data even under transaction costs. \n\nIn view of asset pric e models we consider a stochastic volatility model where the dynamics of t he volatility are described by linear functions of the (time extended) sig nature of a primary underlying process\, which is supposed to be some mult idimensional continuous semimartingale. Under the additional assumption th at this primary process is of polynomial type\, we obtain closed form expr essions for the VIX squared\, exploiting the fact that the truncated signa ture of a polynomial process is again a polynomial process. Adding to such a primary process the Brownian motion driving the stock price\, allows th en to express both the log-price and the VIX squared as linear functions o f the signature of the corresponding augmented process. This feature can t hen be efficiently used for pricing and calibration purposes. Indeed\, as the signature samples can be easily precomputed\, the calibration task ca n be split into an offline sampling and a standard optimization. For both the SPX and VIX options we obtain highly accurate calibration results\, s howing that this model class allows to solve the joint calibration problem without adding jumps or rough volatility.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Christa Cuchiero (University of Vienna) DTSTART:20230331T110000Z DTEND:20230331T130000Z DTSTAMP:20260422T225840Z UID:STochastics_And_Risk/61 DESCRIPTION:Title: Signature methods in finance IV\nby Christa Cuchiero (Un iversity of Vienna) as part of STAR seminars\n\n\nAbstract\nSignature meth ods represent a non-parametric way for extracting characteristic features from time series data which is essential in machine learning tasks. This e xplains why these techniques become more and more popular in Econometrics and Mathematical Finance. Indeed\, signature based approaches allow for da ta-driven and thus more robust model selection mechanisms\, while first pr inciples like no arbitrage can still be easily guaranteed. \n\nIn this cou rse we shall focus on the use of signature as universal linear regression basis of continuous functionals of paths for financial applications. \nWe first give an introduction to continuous rough paths and show how to embed continuous semimartingales into the rough path setting. Indeed our main f ocus lies on signature of semimartingales\, one of the main modeling tools in finance. By relying on the Stone-Weierstrass theorem we show how to pr ove the universal approximation property of linear functions of the signat ure in appropriate topologies on path space. To cover models with jumps we shall additionally introduce the notion of cadlag rough paths\, Marcus si gnature and its universal approximation properties in appropriate Skorokho d topologies. \n\nIn the financial applications that we have in mind one k ey quantity that one needs to compute is the expected signature of some un derlying process. Surprisingly this can be achieved for generic classes of jump diffusions (with possibly path dependent characteristics) via techni ques from affine and polynomial processes. More precisely\, we show how th e signature process of these jump diffusions can be embedded in the framew ork of affine and polynomial processes. These classes of processes have be en -- due to their tractability -- the dominating process class prior to t he new era of highly over-parametrized dynamic models. Following this line we obtain that the infinite dimensional Feynman Kac PIDE of the signature process can generically be reduced to an infinite dimensional ODE either of Riccati or linear type. This then allows to get power series expansion s for the expected signature and the Fourier-Laplace transform. \n\nIn ter ms of financial applications\, we shall treat two main topics: stochastic portfolio theory and signature based asset price models. \n\nIn the contex t of stochastic portfolio theory we introduce a novel class of portfolios which we call linear path-functional portfolios. These are portfolios whic h are determined by certain transformations of linear functions of a colle ctions of feature maps that are non-anticipative path functionals of an un derlying semimartingale. As main example for such feature maps we consider signature of the (ranked) market weights. Relying on the universal approx imation theorem we show that every continuous (possibly path-dependent) p ortfolio function of the market weights can be uniformly approximated by s ignature portfolios. Besides these universality features\, the main numeri cal advantage lies in the fact that several optimization tasks like maximi zing expected logarithmic utility or mean-variance optimization within the class of linear path-functional portfolios reduces to a convex quadratic optimization problem\, thus making it computationally highly tractable. We apply our method to real market data and show generic out-performance on out-of-sample data even under transaction costs. \n\nIn view of asset pric e models we consider a stochastic volatility model where the dynamics of t he volatility are described by linear functions of the (time extended) sig nature of a primary underlying process\, which is supposed to be some mult idimensional continuous semimartingale. Under the additional assumption th at this primary process is of polynomial type\, we obtain closed form expr essions for the VIX squared\, exploiting the fact that the truncated signa ture of a polynomial process is again a polynomial process. Adding to such a primary process the Brownian motion driving the stock price\, allows th en to express both the log-price and the VIX squared as linear functions o f the signature of the corresponding augmented process. This feature can t hen be efficiently used for pricing and calibration purposes. Indeed\, as the signature samples can be easily precomputed\, the calibration task ca n be split into an offline sampling and a standard optimization. For both the SPX and VIX options we obtain highly accurate calibration results\, s howing that this model class allows to solve the joint calibration problem without adding jumps or rough volatility.\n LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/61/ END:VEVENT END:VCALENDAR