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Journal Articles Probability, Uncertainty and Quantitative Risk Year : 2023

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

Abstract

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.
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Dates and versions

hal-02421316 , version 1 (20-12-2019)
hal-02421316 , version 2 (01-11-2022)

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Rui Chen, Roxana Dumitrescu, Andreea Minca, Agnès Sulem. Mean-field BSDEs with jumps and dual representation for global risk measures. Probability, Uncertainty and Quantitative Risk, In press, 8 (1), pp.33-52. ⟨10.3934/puqr.2023002⟩. ⟨hal-02421316v2⟩
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