Backward Stochastic Volterra Integral Equations--- Representation of Adapted Solutions

For backward stochastic Volterra integral equations (BSVIEs, for short), under some mild conditions, the so-called adapted solutions or adapted M-solutions uniquely exist. However, satisfactory regularity of the solutions is difficult to obtain in general. Inspired by the decoupling idea of forward-...

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Bibliographic Details
Main Authors Wang, Tianxiao, Yong, Jiongmin
Format Journal Article
LanguageEnglish
Published 10.02.2018
Subjects
Mathematics - Probability
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Summary:For backward stochastic Volterra integral equations (BSVIEs, for short), under some mild conditions, the so-called adapted solutions or adapted M-solutions uniquely exist. However, satisfactory regularity of the solutions is difficult to obtain in general. Inspired by the decoupling idea of forward-backward stochastic differential equations, in this paper, for a class of BSVIEs, a representation of adapted M-solutions is established by means of the so-called representation partial differential equations and (forward) stochastic differential equations. Well-posedness of the representation partial differential equations are also proved in certain sense.
DOI:10.48550/arxiv.1802.03659