Global existence for quadratic FBSDE systems and application to stochastic differential games

TL;DR

This paper extends recent results on quadratic BSDEs to coupled FBSDE systems in a Markovian setting, using PDE techniques to establish existence and applying these results to stochastic differential games to find Nash equilibria.

Contribution

It introduces a new existence result for coupled quadratic FBSDEs in a Markovian framework and applies it to identify Nash equilibria in stochastic differential games.

Findings

Established existence of solutions for coupled quadratic FBSDEs.

Identified a class of stochastic differential games with Markovian Nash equilibria.

Combined BSDE and PDE techniques for a-priori estimates.

Abstract

In this note, we extend some recent results on systems of backward stochastic differential equations (BSDEs) with quadratic growth to the case of coupled forward-backward stochastic differential equations (FBSDEs). We work in a Markovian setting, and use results from the quadratic BSDE literature together with PDE techniques to obtain a-priori estimates which lead to an existence result. We also identify a general class of stochastic differential games whose corresponding FBSDE systems are covered by our main existence result. This leads to the existence of Markovian Nash equilibria for such games.