Volume 28, 2022
|Number of page(s)||21|
|Published online||26 May 2022|
Dynamic programming principle and Hamilton-Jacobi-Bellman equation under nonlinear expectation
Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan, Shandong 250100, PR China
* Research supported by National Key R&D Program of China (No. 2018YFA0703900) and NSF (No. 11671231).
** Research supported by NSF (No. 11971263 and 11871458).
*** Corresponding author: email@example.com
Accepted: 1 March 2022
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.
Mathematics Subject Classification: 93E20 / 60H10 / 35K15
Key words: Dynamic programming principle / Hamilton-Jacobi-Bellman equation / Stochastic recursive optimal control / Backward stochastic differential equation
© The authors. Published by EDP Sciences, SMAI 2022
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