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.
Type de document :
Pré-publication, Document de travail
2016
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https://hal.archives-ouvertes.fr/hal-01299263
Contributeur : Marie-Annick Guillemer <>
Soumis le : jeudi 7 avril 2016 - 14:21:28
Dernière modification le : vendredi 17 novembre 2017 - 19:14:24

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  • 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〉

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