A BSDE approach to Nash equilibrium payoffs for stochastic differential games with nonlinear cost functionals
Probability
2011-11-30 v2 Optimization and Control
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.
Keywords
Cite
@article{arxiv.1106.1001,
title = {A BSDE approach to Nash equilibrium payoffs for stochastic differential games with nonlinear cost functionals},
author = {Qian Lin},
journal= {arXiv preprint arXiv:1106.1001},
year = {2011}
}