Properties of solution of fractional backward stochastic differential equation

被引：3

作者：

Zhang, Hui ^{[1
]}

机构：

[1] Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan 250014, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 228卷

基金：

中国国家自然科学基金;

关键词：

Backward stochastic differential equation; Fractional Brownian motion; Quasi-conditional expectation; Jensen's inequality; Comparison theorem; Comonotonic theorem; JENSENS INEQUALITY; G-EXPECTATION; DRIVEN;

D O I：

10.1016/j.amc.2013.11.081

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The backward stochastic differential equations (BSDEs) driven by fractional Brownian motion are studied. As an important tool, the quasi-conditional expectation is used. The general forms of Jensen's inequality of quasi-conditional expectation are proved. For the linear BSDEs, their solutions are represented by using the quasi-conditional expectation. Moreover, the comparison theorem and comonotonic theorem of the solutions of linear BSDEs are derived. (c) 2013 Elsevier Inc. All rights reserved.

引用

页码：446 / 453

页数：8

共 11 条

[1]

Biagini F, 2008, PROBAB APPL SER, P1

[2] A comonotonic theorem for BSDEs [J].

Chen, ZJ ;

Kulperger, R ;

Wei, G .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2005, 115 (01) :41-54

[3] Jensen's inequality for g-expectation:: part 1 [J].

Chen, ZJ ;

Kulperger, R ;

Jiang, L .

COMPTES RENDUS MATHEMATIQUE, 2003, 337 (11) :725-730

[4] Jensen's inequality for g-expectation, Part 2 [J].

Chen, ZJ ;

Kulperger, R ;

Jiang, L .

COMPTES RENDUS MATHEMATIQUE, 2003, 337 (12) :797-800

[5] Backward stochastic differential equations in finance [J].

El Karoui, N ;

Peng, S ;

Quenez, MC .

MATHEMATICAL FINANCE, 1997, 7 (01) :1-71

[6] BACKWARD STOCHASTIC DIFFERENTIAL EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION [J].

Hu, Yaozhong ;

Peng, Shige .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (03) :1675-1700

[7] Stochastic control for linear systems driven by fractional noises [J].

Hu, YZ ;

Zhou, XY .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2005, 43 (06) :2245-2277

[8] On Jensen's inequality for g-expectation [J].

Jiang, L ;

Chen, ZJ .

CHINESE ANNALS OF MATHEMATICS SERIES B, 2004, 25 (03) :401-412

[9]

[张慧 Zhang Hui], 2008, [数学物理学报. A辑, Acta Mathematica Scientia], V28, P116

[10]

[张慧 ZHANG Hui], 2008, [中国管理科学, Chinese Journal of Management Science], V16, P25

← 1 2 →