Dynamic programming principle and Hamilton-Jacobi-Bellman equation under nonlinear expectation

In this paper, we study a stochastic recursive optimal control problem in which the value functional is defined by the solution of a backward stochastic differential equation (BSDE) under G-expectation. Under standard assumptions, we establish the comparison theorem for this kind of BSDE and give a...

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Bibliographic Details
Published inESAIM. Control, optimisation and calculus of variations Vol. 28; p. 25
Main Authors Hu, Mingshang, Ji, Shaolin, Li, Xiaojuan
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 2022
Subjects
Differential equations
Dynamic programming
Optimal control
Principles
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Summary:In this paper, we study a stochastic recursive optimal control problem in which the value functional is defined by the solution of a backward stochastic differential equation (BSDE) under G-expectation. Under standard assumptions, we establish the comparison theorem for this kind of BSDE and give a novel and simple method to obtain the dynamic programming principle. Finally, we prove that the value function is the unique viscosity solution to a type of fully nonlinear HJB equation.
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2022019