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

Qian Lin

doi:10.1016/j.spa.2011.08.011

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arXiv · 1106.1001

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

Qian Lin

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Abstract

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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Qian Lin. 2011-08-23. A BSDE approach to Nash equilibrium payoffs for stochastic differential games with nonlinear cost functionals. https://doi.org/10.1016/j.spa.2011.08.011

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