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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Solving Fully Coupled FBSDEs and Stochastic Hamilt
onian Systems via Deep Learning - Ying Peng (Shand
ong University)
DTSTART;TZID=Europe/London:20211116T113000
DTEND;TZID=Europe/London:20211116T120000
UID:TALK165400AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/165400
DESCRIPTION:In this talk\, I will present our recent results o
n numerical solution of high-dimensional Forward b
ackward Stochastic Differential Equations (FBSDEs)
and stochastic control problems via deep learning
.In the field of numerically solving BSDEs\, a wel
l-known challenging problem was "the curse of dime
nsionality". A recent important breakthrough in th
is research direction was made by E et al by using
deep neural network.\nIn this talk\, we present a
type of fully coupled high dimensional FBSDE in w
hich the drift and diffusion coefficient are all g
iven (nonlinear) functions of the backward variabl
es (Y\,Z). In order to solve this type of FBSDE\,
we systematically explore the dependence of the te
rm $Z$ on state precesses $X\,Y$ and even $Z$ itse
lf. Three algorithms corresponding to different ki
nds of state feedback are developed via deep neura
l network and the numerical results demonstrate a
remarkable performance. It is worth to notice that
how to provide an efficient algorithm for this ty
pe of fully coupled nonlinear FBSDE was a largely
open problem.The well-known nonlinear stochastic H
amiltonian system is a typical example of FBSDEs t
hrough which our algorithms have been successfully
applied. We have also developed a direct stochast
ic optimal control approach for solving numericall
y this high dimensional problem. Two different alg
orithms suitable for different cases of the contro
l problem are proposed. The numerical results demo
nstrate more stable convergence comparing with the
FBSDE method for different Hamiltonian systems.In
spired by the deep learning method for solving FBS
DEs\, we also propose a method to solve high dimen
sional stochastic optimal control problem from the
view of the stochastic maximum principle.Joint wo
rk with Prof. Shaolin Ji\, Shige Peng and Dr. Xich
uan Zhang.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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