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Article Dans Une Revue Stochastic Processes and their Applications Année : 2018

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

Résumé

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.

Dates et versions

hal-01299263 , version 1 (07-04-2016)

Identifiants

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Ying Hu, Yiqing Lin, Abdoulaye Soumana-Hima. Quadratic backward stochastic differential equations driven by $G$-Brownian motion: discrete solutions and approximation. Stochastic Processes and their Applications, 2018, 128 (11), pp.3724-3750. ⟨10.1016/j.spa.2017.12.004⟩. ⟨hal-01299263⟩
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