Backward stochastic differential equations driven by G-Brownian motion

被引：131

作者：

Hu, Mingshang ^{[1
]}

Ji, Shaolin ^{[2
]}

Peng, Shige ^{[1
,2
]}

Song, Yongsheng ^{[3
]}

机构：

[1] Shandong Univ, Sch Math, Jinan, Shandong, Peoples R China

[2] Shandong Univ, Qilu Inst Finance, Jinan, Shandong, Peoples R China

[3] Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2014年 / 124卷 / 01期

基金：

中国国家自然科学基金;

关键词：

G-expectation; G-Brownian motion; G-martingale; Backward SDEs; CALCULUS; EXPECTATIONS;

D O I：

10.1016/j.spa.2013.09.010

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 study the backward stochastic differential equations driven by a G-Brownian motion (B-t)(t >= 0) in the following form: Y-t = xi + integral(T)(t) f(s, Y-s, Z(s))d(s) + integral(T)(t) g(s, Y-s, Z(s))d < B >(s) - integral(T)(t) Z(s)dB(s) - (K-T - K-t), where K is a decreasing G.-martingale. Under Lipschitz conditions of f and g in Y and Z, the existence and uniqueness of the solution (Y, Z, K) of the above BSDE in the G-framework is proved. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：759 / 784

页数：26

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