A BSDE approach to Nash equilibrium payoffs for stochastic differential games with nonlinear cost functionals

Details A BSDE approach to Nash equilibrium payoffs for stochastic differential games with nonlinear cost functionals A BSDE approach to Nash equilibrium payoffs for stochastic differential games with nonlinear cost functionals

2011-06-06

arxiv.org/abs/1106.1001v2

Stochastic Processes and their Applications 122 (2012) 357--385

Mathematics

Probability

Scientific paper

10.1016/j.spa.2011.08.011

In this paper, we study Nash equilibrium payoffs for nonzero-sum stochastic differential games via the theory of backward stochastic differential equations. We obtain an existence theorem and a characterization theorem of Nash equilibrium payoffs for nonzero-sum stochastic differential games with nonlinear cost functionals defined with the help of a doubly controlled backward stochastic differential equation. Our results extend former ones by Buckdahn, Cardaliaguet and Rainer (2004) and are based on a backward stochastic differential equation approach.

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