Multi-dimensional BSDEs driven by G-Brownian motion and related system of fully nonlinear PDEs

2018/11/19 by Guomin Liu, Liu, Guomin · 5 citations
Economics, Econometrics and Finance · Mathematics · #60H10 #60H30 #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1811.07773

openalex publication_date 2018/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the well-posedness of multi-dimensional backward stochastic differential equations driven by G-Brownian motion (G-BSDEs) with diagonal generators, the z parts of whose l-th components only depend on the l-th columns. The existence and uniqueness of solutions are obtained via a contraction argument for Y component and a backward iteration of local solutions. Furthermore, we show that, the solution of multi-dimensional G-BSDE in a Markovian framework provides a probabilistic formula for the viscosity solution of a system of nonlinear parabolic partial differential equations.

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• G-BSDEs with non-Lipschitz coefficients and the corresponding stochastic recursive optimal control problem
• Infinite horizon quadratic backward stochastic differential equations driven by G-Brownian motion
• Quadratic BSDEs with double constraints driven by G-Brownian motion

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