Title

Comparison theorems for some backward stochastic Volterra integral equations

Authors

Authors

T. X. Wang;J. M. Yong

Comments

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Abbreviated Journal Title

Stoch. Process. Their Appl.

Keywords

Forward stochastic Volterra integral equations; Backward stochastic; Volterra integral equation; Comparison theorem; Duality principle; MONETARY RISK MEASURES; DIFFERENTIAL-EQUATIONS; ADAPTED SOLUTION; REGULARITY; UTILITY; Statistics & Probability

Abstract

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.

Journal Title

Stochastic Processes and Their Applications

Volume

125

Issue/Number

5

Publication Date

1-1-2015

Document Type

Article

Language

English

First Page

1756

Last Page

1798

WOS Identifier

WOS:000352924100002

ISSN

0304-4149

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