Comparison theorems for some backward stochastic Volterra integral equations

    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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