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

2020/08/12 by Yunhong Li, Anis Matoussi, Li, Yunhong +5
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2008.05426

openalex publication_date 2020/08/12 · openalex created_date 2020/08/18 · openalex updated_date 2026/07/28

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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