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BEGIN:VEVENT
SUMMARY:Fabian Harang (University of Oslo)
DTSTART:20200507T090000Z
DTEND:20200507T100000Z
DTSTAMP:20260422T212558Z
UID:SpringSTORM/1
DESCRIPTION:Title: Deterministic regularization by noise\nby Fabian Harang (Universit
y of Oslo) as part of Spring with STORM\n\nLecture held in Zoom virtual ro
om.\n\nAbstract\nIn this talk we will discuss the concept of regularizatio
n by noise in SDEs from a pathwise point of view. Together with Prof. Nico
las Perkowski at Humboldt University we recently proved that solutions to
ODE's perturbed by a particular irregular (but continuous) path exists uni
quely\, even when the drift vector field of the ODE is only a Scwartz dist
ribution. Moreover\, the flow associated to such perturbed ODE is infinite
ly differentiable. This gives insight into the powerful effect that noise
may have on certain equations. We will also discuss an ongoing extension o
f these results to the regularization by noise towards PDE/SPDEs. By this
we mean that we consider an a-priori ill-posed non-linear PDE/SPDE\, and
show that by perturbation of a sufficiently irregular path\, one obtains w
ell posedness of such equations.\n
LOCATION:https://researchseminars.org/talk/SpringSTORM/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Giordano (University of Oslo)
DTSTART:20200515T090000Z
DTEND:20200515T100000Z
DTSTAMP:20260422T212558Z
UID:SpringSTORM/2
DESCRIPTION:Title: Lifting of Volterra processes: optimal control and HJB equations\n
by Michele Giordano (University of Oslo) as part of Spring with STORM\n\nL
ecture held in Zoom virtual room.\n\nAbstract\nIn this talk we present a n
ew approach to solve an optimization problem with Volterra dynamics driven
by a Brownian motion. Thanks to a lift of the original problem to an infi
nite dimension Banach space\, we are able to recover some Markovian proper
ties\, which in turn allow us to recover the HJB equations for the lifted
problem.\nWith this approach we are thus able to solve the original Volter
ra optimization problem with a "classical" HJB approach.\nJoint work with
Giulia di Nunno\n
LOCATION:https://researchseminars.org/talk/SpringSTORM/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernt Øksendal (University of Oslo)
DTSTART:20200520T090000Z
DTEND:20200520T100000Z
DTSTAMP:20260422T212558Z
UID:SpringSTORM/3
DESCRIPTION:Title: Optimal control of SPDEs with space interactions\nby Bernt Øksend
al (University of Oslo) as part of Spring with STORM\n\nLecture held in Zo
om virtual room.\n\nAbstract\nWe consider optimal control of a new type of
stochastic partial differential equations (SPDEs)\, in which the dynamics
of the system state at a point also depends on the space-mean of values a
t neighbouring points. This is a model with many applications\, e.g. to po
pulation growth studies and epidemiology.\nBoth sufficient and necessary m
aximum principles for the optimal control of such systems are proved. We a
lso prove the existence and uniqueness of solutions of such equations. As
an illustration\, we apply the results to an optimal harvesting problem fr
om a population whose density is modelled as a space-mean stochastic react
ion-diffusion equation.\nThe talk is based on joint works with Nacira Agra
m and Astrid Hilbert\, Linnaeus University (LNU)\, Växjö\, Sweden\n
LOCATION:https://researchseminars.org/talk/SpringSTORM/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Silvia Lavagnini (University of Oslo)
DTSTART:20200529T090000Z
DTEND:20200529T100000Z
DTSTAMP:20260422T212558Z
UID:SpringSTORM/4
DESCRIPTION:Title: Accuracy of deep learning in calibrating HJM forward curves\nby Si
lvia Lavagnini (University of Oslo) as part of Spring with STORM\n\nLectur
e held in Zoom virtual room.\n\nAbstract\nWe price European-style options
written on forward contracts in the commodity market\, which we model with
a state-dependent infinite-dimensional Heath-Jarrow-Morton (HJM) approach
. We introduce a new volatility operator which maps the square integrable
noise into the Filipovi{\\'{c}} space of forward curves\, and we specify a
deterministic parametrized version of it. We train a neural network to ap
proximate the option price as a function of the model parameters. We then
use it to calibrate the HJM parameters starting from (simulated) options m
arket data. Finally we introduce a new loss function taking into account b
id and ask prices\, providing a solution to the liquidity problem. A key i
ssue discovered is that the trained neural network might be non-injective\
, which could potentially lead to poor accuracy in calibrating the forward
curve parameters\, even when showing high degree of accuracy in recoverin
g the prices. This implies that the original meaning of the model paramete
rs gets somehow lost in the approximation step.\nThis is a joint work with
Fred Espen Benth (UiO) and Nils Detering (UCSB).\n
LOCATION:https://researchseminars.org/talk/SpringSTORM/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuela Rosazza-Gianin (University of Milano Bicocca)
DTSTART:20200603T090000Z
DTEND:20200603T100000Z
DTSTAMP:20260422T212558Z
UID:SpringSTORM/5
DESCRIPTION:Title: Capital allocation rules and acceptance sets\nby Emanuela Rosazza-
Gianin (University of Milano Bicocca) as part of Spring with STORM\n\nLect
ure held in Zoom virtual room.\n\nAbstract\nIn the literature\, capital al
location problems are classically studied and associated to risk measures.
The aim of this talk is to introduce a new approach to face capital alloc
ation problems from the perspective of acceptance sets\, by defining the f
amily of sub-acceptance sets.\nWe study the relations between the notions
of sub-acceptability and acceptability of a risky position as well as thei
r impact on capital allocation rules\; in this context\, indeed\, capital
allocation rules are interpretable as tools for assessing the contribution
of a sub-portfolio to a given portfolio in terms of acceptability instead
of necessarily involving a risk measure.\nFurthermore\, we investigate un
der which conditions on a capital allocation rule a representation of an a
cceptance set holds in terms of the capital allocation rule itself in quit
e a general (convex\, quasiconvex\, S-additive) framework.\nFinally\, we i
nvestigate the correspondence between properties at the level of capital a
llocation rules and those at the level of sub-acceptance families.\nThis t
alk is based on a joint work with Gabriele Canna and Francesca Centrone.\n
LOCATION:https://researchseminars.org/talk/SpringSTORM/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Yurchenko-Tytarenko (University of Oslo)
DTSTART:20200612T090000Z
DTEND:20200612T100000Z
DTSTAMP:20260422T212558Z
UID:SpringSTORM/6
DESCRIPTION:Title: Sandwiched processes driven by Hölder noises\nby Anton Yurchenko-
Tytarenko (University of Oslo) as part of Spring with STORM\n\n\nAbstract\
nWe study a stochastic differential equation with an unbounded drift and g
eneral Hölder continuous noise of an arbitrary order. The corresponding e
quation turns out to have a unique solution that\, depending on a particul
ar shape of the drift\, either stays above some continuous function or has
continuous upper and lower bounds. Under some additional assumptions on t
he noise\, we prove that the solution has moments of all orders. Additiona
lly\, numeric schemes for the solution are considered.\nAs illustrations o
f our approach\, generalised CIR and CEV processes will be discussed.\nThi
s talk is based on joint work with Giulia Di Nunno and Yuliya Mishura.\n
LOCATION:https://researchseminars.org/talk/SpringSTORM/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Manuel Corcuera (University of Barcelona)
DTSTART:20200617T090000Z
DTEND:20200617T100000Z
DTSTAMP:20260422T212558Z
UID:SpringSTORM/7
DESCRIPTION:Title: Path-dependent Kyle equilibrium model\nby José Manuel Corcuera (U
niversity of Barcelona) as part of Spring with STORM\n\n\nAbstract\nKyle m
odel is a classic model to explain the formation of prices\nin a financial
market. It is assumed that prices increase with the total\ndemand of the
stock and market makers provide liquidity in the market and\nfix the price
s in a competitive way. The demand comes from noise traders and\nits is as
sumed the presence of an informed trader who knows the liquidation\nvalue
of the stock. This informed trader tries to optimize their strategy.\nWhen
all the actors are satisfied then we say that we have an equilibrium.\nDi
fferent kind of equilibriums have been obtained under the assumption that\
nprices depend on the spot value of the total demand or a particular\npath
-dependence. In this work\, inspired by the functional It\\^{o} calculus\,
\nwe study the equilibrium when prices are a functional of the path of the
\naggregate demand in a very general form. We consider the case when the\n
informed trader is risk neutral as well as the risk-averse case.\n\nThis i
s joint work with Giulia di Nunno and Jos\\'{e} Fajardo who sadly\npassed
away this third of May.\n
LOCATION:https://researchseminars.org/talk/SpringSTORM/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dennis Schoers (University of Oslo)
DTSTART:20200626T090000Z
DTEND:20200626T100000Z
DTSTAMP:20260422T212558Z
UID:SpringSTORM/8
DESCRIPTION:Title: Copulas and Sklar's theorem in infinite dimensions\nby Dennis Scho
ers (University of Oslo) as part of Spring with STORM\n\nAbstract: TBA\n\n
Copulas describe statistical dependence between the components of multivar
iate random variables in full generality by virtue of Sklar’s theorem. A
lthough they are used and defined for certain infinite dimensional objects
(e.g. Gaussian processes\, Markov processes or infinite dimensional Archi
medean copulas) there is no prevalent notion of a copula as an infinite di
mensional law that unifies these concepts. To this end we define copulas a
s probability measures on product spaces and prove Sklar’s theorem in th
is general setting.\nAfterwards we use this result on Banach spaces to con
struct cylindrical probability measures with predefined marginals and unde
rlying copula. This induces the functional analytic problem of finding cri
teria in which cases the obtained cylindrical law induces a real probabili
ty measure\, which is in general difficult to decide. We solve this proble
m in the p-Wasserstein space on the space of p-summable sequences (in- clu
ding separable Hilbert spaces) and show that copulas effectively solve a r
estricted optimal coupling problem.\nThis is joint work with Fred Espen Be
nth and Giulia Di Nunno\n
LOCATION:https://researchseminars.org/talk/SpringSTORM/8/
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