Volume 24, Number 2, April–June 2018
|Page(s)||873 - 899|
|Published online||13 June 2018|
Stochastic optimal control problem with infinite horizon driven by G-Brownian motion★
Zhongtai Securities Institute for Financial Studies, Shandong University,
2 Zhongtai Securities Institute for Financial Studies and Institute for Advanced Research, Shandong University, Jinan 250100, China
a Corresponding author: firstname.lastname@example.org
Revised: 25 January 2017
Accepted: 10 June 2017
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.
Mathematics Subject Classification: 93E20 / 60H10 / 35J60
Key words: G-Brownian motion / backward stochastic differential equations / stochastic optimal control / dynamic programming principle
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)
© EDP Sciences, SMAI 2018
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