Abstract and Applied Analysis
Volume 2013 (2013), Article ID 761306, 7 pages
http://dx.doi.org/10.1155/2013/761306
Research Article

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

Yan Wang,1,2 Aimin Song,2 Cheng-De Zheng,2 and Enmin Feng1

1School of Mathematical Sciences, Dalian University of Technology, Dalian 116023, China
2School of Science, Dalian Jiaotong University, Dalian 116028, China

Received 5 February 2013; Accepted 7 May 2013

Academic Editor: Ryan Loxton

Copyright © 2013 Yan Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.