Non-zero Sum Stochastic Differential Games of Fully Coupled Forward-Backward Stochastic Systems

2010/10/12 by Maoning Tang, Qingxin Meng, Tang, Maoning +3
Economics, Econometrics and Finance · Mathematics · Social Sciences · #Insurance, Mortality, Demography, Risk Management #Mathematical Biology Tumor Growth #Stochastic processes and financial applications #math.OC

paper · pdf · doi:10.48550/arxiv.1010.2306

arxiv created 2010/10/12 · arxiv updated 2010/10/13

Abstract

In this paper, an open-loop two-person non-zero sum stochastic differential game is considered for forward-backward stochastic systems. More precisely, the controlled systems are described by a fully coupled nonlinear multi- dimensional forward-backward stochastic differential equation driven by a multi-dimensional Brownian motion. one sufficient (a verification theorem) and one necessary conditions for the existence of open-loop Nash equilibrium points for the corresponding two-person non-zero sum stochastic differential game are proved. The control domain need to be convex and the admissible controls for both players are allowed to appear in both the drift and diffusion of the state equations.

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