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

Hu, Mingshang; Ji, Shaolin; Li, Xiaojuan

ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 25

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.

Classification : 93E20, 60H10, 35K15
Keywords: Dynamic programming principle, Hamilton-Jacobi-Bellman equation, Stochastic recursive optimal control, Backward stochastic differential equation

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