SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS

doi:10.1016/S0252-9602(18)30774-4

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (2): 681-694.doi: 10.1016/S0252-9602(18)30774-4

SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS

韩月才¹, 孙一芳²

1. Department of Mathematical Finance, School of Mathematics, Jilin University, Changchun 130012, China;
2. Department of Probability and Mathematical Statistics, School of Mathematics, Jilin University, Changchun 130012, China

收稿日期:2016-11-28 修回日期:2017-05-18 出版日期:2018-04-25 发布日期:2018-04-25
通讯作者: Yifang SUN E-mail:syf15@mails.jlu.edu.cn
作者简介:Yuecai HAN,E-mail:hanyc@jlu.edu.cn
基金资助:
This work was supported by NSFC grant (11371169), and China Automobile Industry Innovation and Development Joint Fund (U1564213).

SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS

Yuecai HAN¹, Yifang SUN²

1. Department of Mathematical Finance, School of Mathematics, Jilin University, Changchun 130012, China;
2. Department of Probability and Mathematical Statistics, School of Mathematics, Jilin University, Changchun 130012, China

Received:2016-11-28 Revised:2017-05-18 Online:2018-04-25 Published:2018-04-25
Contact: Yifang SUN E-mail:syf15@mails.jlu.edu.cn
Supported by:
This work was supported by NSFC grant (11371169), and China Automobile Industry Innovation and Development Joint Fund (U1564213).

摘要/Abstract

摘要：

The local existence and uniqueness of the solutions to backward stochastic differential equations(BSDEs, in short) driven by both fractional Brownian motions with Hurst parameter H∈(1/2,1) and the underlying standard Brownian motions are studied. The generalization of the Itô formula involving the fractional and standard Brownian motions is provided. By theory of Malliavin calculus and contraction mapping principle, the local existence and uniqueness of the solutions to BSDEs driven by both fractional Brownian motions and the underlying standard Brownian motions are obtained.

关键词: Backward stochastic differential equations, malliavin calculus, fractional Brownian motions, Itô, formula

Abstract:

Key words: Backward stochastic differential equations, malliavin calculus, fractional Brownian motions, Itô, formula

韩月才, 孙一芳. SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS[J]. 数学物理学报(英文版), 2018, 38(2): 681-694.

Yuecai HAN, Yifang SUN. SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS[J]. Acta mathematica scientia,Series B, 2018, 38(2): 681-694.

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SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS

SOLUTIONS TO BSDES DRIVEN BY BOTH FRACTIONAL BROWNIAN MOTIONS AND THE UNDERLYING STANDARD BROWNIAN MOTIONS

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