Quadratic backward stochastic differential equations driven by G-Brownian motion: Discrete solutions and approximation

Ying Hu, Yiqing Lin and Abdoulaye Soumana Hima

Stochastic Processes and their Applications, 2018, vol. 128, issue 11, 3724-3750

Abstract: In this paper, we consider backward stochastic differential equations driven by G-Brownian motion (GBSDEs) under quadratic assumptions on coefficients. We prove the existence and uniqueness of solution for such equations. On the one hand, a priori estimates are obtained by applying the Girsanov type theorem in the G-framework, from which we deduce the uniqueness. On the other hand, to prove the existence of solutions, we first construct solutions for discrete GBSDEs by solving corresponding fully nonlinear PDEs, and then approximate solutions for general quadratic GBSDEs in Banach spaces.

Keywords: Backward stochastic differential equations; Quadratic growth; G-Brownian motion; Discretization; Fully nonlinear PDEs (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:11:p:3724-3750

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DOI: 10.1016/j.spa.2017.12.004

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