Abstract
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.
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This paper was supported by the National Natural Science Foundation of China (11901184, 11771343) and the Natural Science Foundation of Hunan Province (2020JJ5025).
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Miao, L., Chen, Y., Xiao, X. et al. Anticipated Backward Stochastic Volterra Integral Equations with Jumps and Applications to Dynamic Risk Measures. Acta Math Sci 43, 1365–1381 (2023). https://doi.org/10.1007/s10473-023-0321-2
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DOI: https://doi.org/10.1007/s10473-023-0321-2