Abstract
We study optimal stochastic control problems 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 assumptions on the SDE. We develop a control 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 $G$-expectation.
Citation
Marco Fuhrman. Huyên Pham. "Randomized and backward SDE representation for optimal control of non-Markovian SDEs." Ann. Appl. Probab. 25 (4) 2134 - 2167, August 2015. https://doi.org/10.1214/14-AAP1045
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