Solvability of anticipated backward stochastic Volterra integral equations

In this paper, we focus on a new class of equations called the anticipated backward stochastic Volterra integral equations (ABSVIEs, for short). In this class of equations, the generator involves not only the present information of the solution but also its future one. Under the Lipschitz condition,...

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Bibliographic Details
Published inStatistics & probability letters Vol. 156; p. 108599
Main Authors Wen, Jiaqiang, Shi, Yufeng
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.01.2020
Subjects
Anticipated generator
Backward stochastic differential equation
Backward stochastic Volterra integral equation
Time-advanced
Time-advanced
60H10
Backward stochastic Volterra integral equation
60H20
Backward stochastic differential equation
Anticipated generator
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Summary:In this paper, we focus on a new class of equations called the anticipated backward stochastic Volterra integral equations (ABSVIEs, for short). In this class of equations, the generator involves not only the present information of the solution but also its future one. Under the Lipschitz condition, we obtain the existence and uniqueness of the adapted M-solutions. Meanwhile, a comparison theorem is also proved.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2019.108599