Nash equilibrium payoffs for stochastic differential games with reflection

TL;DR

This paper studies Nash equilibrium payoffs in nonzero-sum stochastic differential games involving reflection, providing existence and characterization theorems for such equilibria using doubly controlled reflected backward stochastic differential equations.

Contribution

It introduces a novel framework for analyzing Nash equilibria in stochastic differential games with reflection, extending existing theories to nonlinear cost functionals.

Findings

Existence theorem for Nash equilibrium payoffs.

Characterization theorem for Nash equilibrium payoffs.

Application of doubly controlled reflected backward stochastic differential equations.

Abstract

In this paper, we investigate Nash equilibrium payoffs for nonzero-sum stochastic differential games with reflection. We obtain an existence theorem and a characterization theorem of Nash equilibrium payoffs for nonzero-sum stochastic differential games with nonlinear cost functionals defined by doubly controlled reflected backward stochastic differential equations.