Comparison theorems for some backward stochastic Volterra integral equations

被引：31
作者：
Wang, Tianxiao [1 ]
Yong, Jiongmin [2 ]
机构：
[1] Sichuan Univ, Sch Math, Chengdu 610065, Peoples R China
[2] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2015年 / 125卷 / 05期
基金：
美国国家科学基金会;
关键词：
Forward stochastic Volterra integral equations; Backward stochastic Volterra integral equation; Comparison theorem; Duality principle; MONETARY RISK MEASURES; DIFFERENTIAL-EQUATIONS; ADAPTED SOLUTION; REGULARITY;
D O I：
10.1016/j.spa.2014.11.013
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：
For some backward stochastic Volterra integral equations (BSVIEs) in multi-dimensional Euclidean spaces, comparison theorems are established in a systematic way for the adapted solutions and adapted M-solutions. For completeness, comparison theorems for (forward) stochastic differential equations, backward stochastic differential equations, and (forward) stochastic Volterra integral equations (FSVIEs) are also presented. Duality principles are used in some relevant proofs. Also, it is found that certain kinds of monotonicity conditions play crucial roles to guarantee the comparison theorems for FSVIEs and BSVIEs to be true. Various counterexamples show that the assumed conditions are almost necessary in some sense. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：1756 / 1798
页数：43
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