Nash Equilibrium Payoffs for Stochastic Differential Games with two Reflecting Barriers

Abstract

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

Non-semimartingale solutions of reflected BSDEs and applications to Dynkin games

“…Since then the notion of reflected BSDEs was recognized as a very useful and important tool in application to stochastic control, mathematical finance and the variational inequalities theory (see e.g. [8,23,27,32,33,39] and reference therein). Subsequently, in many papers the assumptions adopted in [11] were weakened but the separation condition (called Mokobodzki's condition) was always assumed (see Remark 2.8).…”