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

被引：21

作者：

Hu, Ying ^{[1
]}

Lin, Yiqing ^{[2
,3
]}

Hima, Abdoulaye Soumana ^{[1
,4
]}

机构：

[1] Univ Rennes 1, Inst Rech Math Rennes, F-35042 Rennes, France

[2] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

[3] Ecole Polytech, Ctr Math Appl, F-91128 Palaiseau, France

[4] Univ Maradi, Dept Math, BP 465, Maradi, Niger

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2018年 / 128卷 / 11期

基金：

欧洲研究理事会; 中国国家自然科学基金;

关键词：

Backward stochastic differential equations; Quadratic growth; G-Brownian motion; Discretization; Fully nonlinear PDEs; FEYNMAN-KAC FORMULA; G-EXPECTATION; REPRESENTATION THEOREM; BSDES; GROWTH; CALCULUS; COEFFICIENTS; FRAMEWORK; SPACES;

D O I：

10.1016/j.spa.2017.12.004

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：3724 / 3750

页数：27

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