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arXiv · 2106.02814

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

Mingshang Hu·Shaolin Ji·Xiaojuan Li
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Abstract

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 $\tilde{G}$-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 of a type of fully nonlinear HJB equation.

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Mingshang Hu, Shaolin Ji, Xiaojuan Li. 2021-06-05. Dynamic programming principle and Hamilton-Jacobi-Bellman equation under nonlinear expectation. https://arxiv.org/abs/2106.02814

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