Dynamic Programming Principle for Backward Doubly Stochastic Recursive Optimal Control Problem and Sobolev Weak Solution of The Stochastic Hamilton-Bellman Equation

Yunhong Li; Anis. Matoussi; Lifeng Wei; Zhen Wu

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arXiv · 2008.05426

Dynamic Programming Principle for Backward Doubly Stochastic Recursive Optimal Control Problem and Sobolev Weak Solution of The Stochastic Hamilton-Bellman Equation

Yunhong Li·Anis. Matoussi·Lifeng Wei·Zhen Wu

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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.

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Yunhong Li, Anis. Matoussi, Lifeng Wei, Zhen Wu. 2020-08-12. Dynamic Programming Principle for Backward Doubly Stochastic Recursive Optimal Control Problem and Sobolev Weak Solution of The Stochastic Hamilton-Bellman Equation. https://arxiv.org/abs/2008.05426

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