| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 25 | |
| Number of page(s) | 21 | |
| DOI | https://doi.org/10.1051/cocv/2022019 | |
| 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: lixiaojuan@mail.sdu.edu.cn
Received:
15
June
2021
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
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.