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

2021/10/04 by Joe Jackson, Jackson, Joe
Economics, Econometrics and Finance · #Climate Change Policy and Economics #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2110.01588

openalex publication_date 2021/10/04 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

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.

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