Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions

Abstract and Applied Analysis

Research Article

Enmin Feng¹  Cheng-De Zheng³  Aimin Song³  Yan Wang² 

[1] School of Mathematical Sciences, Dalian University of Technology, Dalian 116023, China, dlut.edu.cn;School of Mathematical Sciences, Dalian University of Technology, Dalian 116023, China, dlut.edu.cn;School of Science, Dalian Jiaotong University, Dalian 116028, China, djtu.edu.cn;School of Science, Dalian Jiaotong University, Dalian 116028, China, djtu.edu.cn

Others  :  1297443
DOI  :  10.1155/2013/761306

 received in 2013-02-05, accepted in 2013-05-07,  发布年份 2013

【 摘 要 】

We consider a nonzero-sum stochastic differential game which involves two players, a controller and a stopper. The controller chooses a control process, and the stopper selects the stopping rule which halts the game. This game is studied in a jump diffusions setting within Markov control limit. By a dynamic programming approach, we give a verification theorem in terms of variational inequality-Hamilton-Jacobi-Bellman (VIHJB) equations for the solutions of the game. Furthermore, we apply the verification theorem to characterize Nash equilibrium of the game in a specific example.

【 授权许可】

CC BY   
Copyright © 2013 Yan Wang et al. 2013

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