Nonzero-Sum Stochastic Differential Game between Controller and Stopper for Jump Diffusions. (16th May 2013)

• Record Type: Journal Article
• Authors: Wang, Yan; Song, Aimin; Zheng, Cheng-De; Feng, Enmin
• Other Names: Loxton Ryan Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-05-16
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/761306
• Languages: English
• ISSNs: 1085-3375

Abstract

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.