A BSDE Approach to Stochastic Differential Games Involving Impulse Controls and HJBI Equation

被引：0
作者：
Liangquan Zhang
机构：
[1] Beijing University of Posts and Telecommunications,School of Science
来源：
Journal of Systems Science and Complexity | 2022年 / 35卷
关键词：
Dynamic programming principle (DPP); forward-backward stochastic differential equations (FBSDEs); Hamilton-Jacobi-Bellman-Isaacs (HJBI); impulse control; stochastic differential games; value function; viscosity solution;
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学科分类号：
摘要：
This paper focuses on zero-sum stochastic differential games in the framework of forward-backward stochastic differential equations on a finite time horizon with both players adopting impulse controls. By means of BSDE methods, in particular that of the notion from Peng’s stochastic backward semigroups, the authors prove a dynamic programming principle for both the upper and the lower value functions of the game. The upper and the lower value functions are then shown to be the unique viscosity solutions of the Hamilton-Jacobi-Bellman-Isaacs equations with a double-obstacle. As a consequence, the uniqueness implies that the upper and lower value functions coincide and the game admits a value.
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页码：766 / 801
页数：35
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