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BEGIN:VEVENT
SUMMARY:Andreas Petersson (University of Oslo)
DTSTART;VALUE=DATE-TIME:20200918T090000Z
DTEND;VALUE=DATE-TIME:20200918T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20200925T090000Z
DTEND;VALUE=DATE-TIME:20200925T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20201002T090000Z
DTEND;VALUE=DATE-TIME:20201002T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20201009T090000Z
DTEND;VALUE=DATE-TIME:20201009T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20201016T090000Z
DTEND;VALUE=DATE-TIME:20201016T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20201023T090000Z
DTEND;VALUE=DATE-TIME:20201023T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20201106T100000Z
DTEND;VALUE=DATE-TIME:20201106T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20201113T100000Z
DTEND;VALUE=DATE-TIME:20201113T111500Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20201218T100000Z
DTEND;VALUE=DATE-TIME:20201218T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20201120T100000Z
DTEND;VALUE=DATE-TIME:20201120T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20201204T100000Z
DTEND;VALUE=DATE-TIME:20201204T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20210115T100000Z
DTEND;VALUE=DATE-TIME:20210115T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20210129T100000Z
DTEND;VALUE=DATE-TIME:20210129T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20210212T100000Z
DTEND;VALUE=DATE-TIME:20210212T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20210219T100000Z
DTEND;VALUE=DATE-TIME:20210219T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20210305T100000Z
DTEND;VALUE=DATE-TIME:20210305T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20210319T100000Z
DTEND;VALUE=DATE-TIME:20210319T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20210430T090000Z
DTEND;VALUE=DATE-TIME:20210430T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20210416T090000Z
DTEND;VALUE=DATE-TIME:20210416T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20210507T090000Z
DTEND;VALUE=DATE-TIME:20210507T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20210521T090000Z
DTEND;VALUE=DATE-TIME:20210521T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20210611T090000Z
DTEND;VALUE=DATE-TIME:20210611T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20210820T090000Z
DTEND;VALUE=DATE-TIME:20210820T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20210917T090000Z
DTEND;VALUE=DATE-TIME:20210917T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20211001T090000Z
DTEND;VALUE=DATE-TIME:20211001T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20210903T090000Z
DTEND;VALUE=DATE-TIME:20210903T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20211015T090000Z
DTEND;VALUE=DATE-TIME:20211015T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20211105T090000Z
DTEND;VALUE=DATE-TIME:20211105T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20211105T100000Z
DTEND;VALUE=DATE-TIME:20211105T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20211109T121500Z
DTEND;VALUE=DATE-TIME:20211109T130000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20211112T080000Z
DTEND;VALUE=DATE-TIME:20211112T160000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20211210T090000Z
DTEND;VALUE=DATE-TIME:20211210T100000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20211125T070000Z
DTEND;VALUE=DATE-TIME:20211125T140000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20211126T070000Z
DTEND;VALUE=DATE-TIME:20211126T140000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20211210T100000Z
DTEND;VALUE=DATE-TIME:20211210T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20220121T100000Z
DTEND;VALUE=DATE-TIME:20220121T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20220204T100000Z
DTEND;VALUE=DATE-TIME:20220204T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
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;VALUE=DATE-TIME:20220218T100000Z
DTEND;VALUE=DATE-TIME:20220218T110000Z
DTSTAMP;VALUE=DATE-TIME:20220128T031229Z
UID:STochastics_And_Risk/38
DESCRIPTION:by Colin Ramsay (University of Nebraska-Lincoln) as part of ST
AR seminars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/STochastics_And_Risk/38/
END:VEVENT
END:VCALENDAR