Dual and backward SDE representation for optimal control of non-Markovian SDEs
Probability
2013-11-04 v1
Abstract
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 develop a controls randomization approach, and prove that the value function can be reformulated under a family of dominated measures on an enlarged filtered probability space. This value function is then 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 equation, and an extension to expectation.
Keywords
Cite
@article{arxiv.1310.6943,
title = {Dual and backward SDE representation for optimal control of non-Markovian SDEs},
author = {Marco Fuhrman and Huyên Pham},
journal= {arXiv preprint arXiv:1310.6943},
year = {2013}
}