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ANTICIPATED BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS WITH JUMPS AND APPLICATIONS TO dynamic risk measures

Acta Mathematica Scientia 2023年第3期43卷 1365-1381页

作者：缪亮亮陈燕红肖肖胡亦钧 School of Mathematics and Information Technology Jiangsu Second Normal UniversityNanjing210013China College of Finance and Statistics Hunan UniversityChangsha410082China School of Mathematics and Statistics Wuhan UniversityWuhan430072China

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.

关键词： anticipated backward stochastic Volterra integral equations comparison theorems dynamic risk measures

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Mean-field BSDEs with jumps and dual representation for global risk measures

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Probability, Uncertainty and Quantitative risk 2023年第1期8卷 33-52页

作者： Rui Chen Roxana Dumitrescu Andreea Minca Agnès Sulem INRIA Paris 2 rue Simone IffCS 4211275589 ParisCedex 12France UniversitéParis-Dauphine 75775 ParisCedex 16France Department of Mathematics King’s College LondonStrandLondon WC 2 R 2LSUK Department of Operations Research and Information Engineering Cornell University222 Rhodes HallIthacaNY 14853USA

We study mean-field BSDEs with jumps and a generalized mean-field operator that can capture higher-order interactions.We interpret the BSDE solution as a dynamic risk measure for a representative bank whose risk attitude is influenced by the system.This influence can come in a wide class of choices,including the average system state or average intensity of system interactions.Using Fenchel−Legendre transforms,our main result is a dual representation for the expectation of the risk measure in the convex case.In particular,we exhibit its dependence on the mean-field operator.

关键词： Mean-field interactions BSDEs dynamic risk measures System influence

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