Dynamic Programming Principle for Backward Doubly Stochastic Recursive Optimal Control Problem and Sobolev Weak Solution of The Stochastic Hamilton-Bellman Equation
Probability
2020-08-13 v1 Optimization and Control
Abstract
In this paper, we study backward doubly stochastic recursive optimal control problem where the cost function is described by the solution of a backward doubly stochastic differential equation. We give the dynamical programming principle for this kind of optimal control problem and show that the value function is the unique Sobolev weak solution for the corresponding stochastic Hamilton-Jacobi-Bellman equation.
Cite
@article{arxiv.2008.05426,
title = {Dynamic Programming Principle for Backward Doubly Stochastic Recursive Optimal Control Problem and Sobolev Weak Solution of The Stochastic Hamilton-Bellman Equation},
author = {Yunhong Li and Anis. Matoussi and Lifeng Wei and Zhen Wu},
journal= {arXiv preprint arXiv:2008.05426},
year = {2020}
}