Anticipated Backward Stochastic Volterra Integral Equations with Jumps and Applications to Dynamic Risk Measures

In this paper, we focus on anticipated backward stochastic Volterra integral equations (ABSVIEs) with jumps. We solve the problem of the well-posedness of so-called M-solutions to this class of equation, and analytically derive a comparison theorem for them and for the continuous equilibrium consump...

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Bibliographic Details
Published in:Acta mathematica scientia 2023-05, Vol.43 (3), p.1365-1381
Main Authors: Miao, Liangliang, Chen, Yanhong, Xiao, Xiao, Hu, Yijun
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:In this paper, we focus on anticipated backward stochastic Volterra integral equations (ABSVIEs) with jumps. We solve the problem of the well-posedness of so-called M-solutions to this class of equation, and analytically derive a comparison theorem for them and for the continuous equilibrium consumption process. These continuous equilibrium consumption processes can be described by the solutions to this class of ABSVIE with jumps. Motivated by this, a class of dynamic risk measures induced by ABSVIEs with jumps are discussed.
ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-023-0321-2