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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 718714, 15 pages
http://dx.doi.org/10.1155/2012/718714
Research Article

Stochastic Recursive Zero-Sum Differential Game and Mixed Zero-Sum Differential Game Problem

1School of Mathematical Sciences, Ocean University of China, Qingdao 266003, China
2School of Mathematics, Shandong University, Jinan 250100, China

Received 4 October 2012; Accepted 10 December 2012

Academic Editor: Guangchen Wang

Copyright © 2012 Lifeng Wei and Zhen Wu. 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

Under the notable Issacs's condition on the Hamiltonian, the existence results of a saddle point are obtained for the stochastic recursive zero-sum differential game and mixed differential game problem, that is, the agents can also decide the optimal stopping time. The main tools are backward stochastic differential equations (BSDEs) and double-barrier reflected BSDEs. As the motivation and application background, when loan interest rate is higher than the deposit one, the American game option pricing problem can be formulated to stochastic recursive mixed zero-sum differential game problem. One example with explicit optimal solution of the saddle point is also given to illustrate the theoretical results.