Recursive stochastic linear-quadratic optimal control and nonzero-sum differential game problems with random jumps

Advances in Difference Equations

Na Li¹  Zhiyong Yu² 

[1] Department of Mathematics, QiLu Normal University, Jinan, China;School of Mathematics, Shandong University, Jinan, China

关键词: forward-backward stochastic differential equation;    Poisson process;    stochastic optimal control;    linear-quadratic problem;    nonzero-sum stochastic differential game;    Nash equilibrium;    60H10;    93E20;    91A15;   

DOI  :  10.1186/s13662-015-0439-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper presents an existence and uniqueness result for a kind of forward-backward stochastic differential equations (FBSDEs for short) driven by Brownian motion and Poisson process under some monotonicity conditions. By virtue of the conclusion of FBSDEs, we solve a linear-quadratic stochastic optimal control problem for forward-backward stochastic systems with random jumps. Moreover, we also solve a linear-quadratic nonzero-sum stochastic differential game problem. We obtain explicit forms of the unique optimal control and the unique Nash equilibrium point, respectively.

【 授权许可】

CC BY