# Quadratic backward stochastic differential equations driven by $G$-Brownian motion: discrete solutions and approximation

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 :
Type de document :
Pré-publication, Document de travail
2016
Domaine :

https://hal.archives-ouvertes.fr/hal-01299263
Contributeur : Marie-Annick Guillemer <>
Soumis le : jeudi 7 avril 2016 - 14:21:28
Dernière modification le : mardi 26 juin 2018 - 08:14:04

### Identifiants

• HAL Id : hal-01299263, version 1
• ARXIV : 1603.03637

### Citation

Ying Hu, Yiqing Lin, Abdoulaye Soumana-Hima. Quadratic backward stochastic differential equations driven by $G$-Brownian motion: discrete solutions and approximation. 2016. 〈hal-01299263〉

### Métriques

Consultations de la notice