Huyên Pham - Randomization approach for stochastic control problems
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2014-04-02

Huyên Pham (Université Paris Diderot)
We study optimal stochastic control problem for non-Markovian stochastic differential 
equations (SDEs) where the drift, diffusion coefficients, and gain functionals are path-dependent, 
and importantly we do not make any ellipticity assumption on the SDE. We present a 
randomization approach of the control, and prove that the value function can be characterized by a 
backward SDE with nonpositive jumps under a single probability measure, which can be viewed as 
a path-dependent version of the Hamilton-Jacobi-Bellman (HJB) equation, and an extension to G-expectation. This includes in particular equations in finance arising from model uncertainty. In the 
Markovian case, our BSDE representation provides a Feynman-Kac type formula to fully nonlinear 
HJB equation, and leads to a new probabilistic numerical scheme for solving this equation, taking 
advantage of high dimensional features of Monte-Carlo methods.