Stochastic optimal control problem with infinite horizon driven by G-Brownian motion

The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of the value function and establish the dynamic programming pr...

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Published inESAIM. Control, optimisation and calculus of variations Vol. 24; no. 2; pp. 873 - 899
Main Authors Hu, Mingshang, Wang, Falei
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 01.04.2018
Subjects
35J60
60H10
93E20
backward stochastic differential equations
Brownian motion
Differential equations
Dynamic programming
dynamic programming principle
G-Brownian motion
Optimal control
Stochastic control theory
stochastic optimal control
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Summary:The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of the value function and establish the dynamic programming principle. Moreover, we prove that the value function is the unique viscosity solution of the related Hamilton−Jacobi−Bellman−Isaacs (HJBI) equation.
Bibliography:href:https://www.esaim-cocv.org/articles/cocv/abs/2018/02/cocv160089/cocv160089.html
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Falei Wang is the corresponding author. Hu's research was supported by the National Natural Science Foundation of China (No. 11671231) and the Young Scholars Program of Shandong University (No. 2016WLJH10). Wang's research was supported by the National Natural Science Foundation of China (No. 11601282), the Natural Science Foundation of Shandong Province (No. ZR2016AQ10) and the Fundamental Research Funds of Shandong University (No. 2015GN023). Hu and Wang's research was partially supported by the Tian Yuan Projection of the National Natural Sciences Foundation of China (Nos. 11526205 and 11626247) and the 111 Project (No. B12023)
publisher-ID:cocv160089
humingshang@sdu.edu.cn
istex:F00A0B058D95051B1FFF1FE1EAD083F5976C5355
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2017044