Explicit solutions of a class of linear fractional BSDEs

被引：28

作者：

Bender, C ^{[1
]}

机构：

[1] Weierstrass Inst Appl Anal & Stochastics, D-10117 Berlin, Germany

来源：

SYSTEMS & CONTROL LETTERS | 2005年 / 54卷 / 07期

关键词：

backward stochastic differential equations; fractional Brownian motion; partial differential equations;

D O I：

10.1016/j.sysconle.2004.11.006

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We obtain explicit solutions for a class of linear backward stochastic differential equations driven by a fractional Brownian motion with arbitrary Hurst parameter via the solution of a partial differential equation and a fractional U formula. (c) 2004 Elsevier B.V. All rights reserved.

引用

页码：671 / 680

页数：10

共 12 条

[1] Stochastic calculus with respect to Gaussian processes
Alòs, E
Mazet, O
Nualart, D
[J]. ANNALS OF PROBABILITY, 2001, 29 (02) : 766 - 801
[2] An S-transform approach to integration with respect to a fractional Brownian motion
Bender, C
[J]. BERNOULLI, 2003, 9 (06) : 955 - 983
[3] An Ito formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter
Bender, C
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2003, 104 (01) : 81 - 106
[4] Bender C., 2003, STOCH STOCH REP, V75, P391
[5] A stochastic maximum principle for processes driven by fractional Brownian motion
Biagini, F
Hu, YZ
Oksendal, B
Sulem, A
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2002, 100 : 233 - 253
[6] A general fractional white noise theory and applications to finance
Elliott, RJ
van der Hoek, J
[J]. MATHEMATICAL FINANCE, 2003, 13 (02) : 301 - 330
[7] On the prediction of fractional Brownian motion
Gripenberg, G
Norros, I
[J]. JOURNAL OF APPLIED PROBABILITY, 1996, 33 (02) : 400 - 410
[8] Hille Einar, 1957, Functional analysis and semigroups, V31
[9] Fractional white noise calculus and applications to finance
Hu, YZ
Oksendal, B
[J]. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2003, 6 (01) : 1 - 32
[10] SOLVING FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL-EQUATIONS EXPLICITLY - A 4 STEP SCHEME
MA, J
PROTTER, P
YONG, JM
[J]. PROBABILITY THEORY AND RELATED FIELDS, 1994, 98 (03) : 339 - 359

← 1 2 →