Regularity of Backward Stochastic Volterra Integral Equations in Hilbert Spaces

被引：14

作者：

Anh, Vo V. ^{[1
]}

Grecksch, Wilfried ^{[2
]}

Yong, Jiongmin ^{[3
]}

机构：

[1] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia

[2] Univ Halle Wittenberg, Inst Math, Halle, Saale, Germany

[3] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA

来源：

STOCHASTIC ANALYSIS AND APPLICATIONS | 2011年 / 29卷 / 01期

基金：

美国国家科学基金会; 澳大利亚研究理事会;

关键词：

Pontryagin maximum principle; Regularity of adapted solutions; Stochastic optimal control; Stochastic Volterra integral equations; COHERENT; DRIVEN;

D O I：

10.1080/07362994.2011.532046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article investigates backward stochastic Volterra integral equations in Hilbert spaces. The existence and uniqueness of their adapted solutions is reviewed. We establish the regularity of the adapted solutions to such equations by means of Malliavin calculus. For an application, we study an optimal control problem for a stochastic Volterra integral equation driven by a Hilbert space-valued fractional Brownian motion. A Pontryagin-type maximum principle is formulated for the problem and an example is presented.

引用

页码：146 / 168

页数：23

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