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

Rui Chen (1, 2) , Roxana Dumitrescu (3) , Andreea Minca (4) , Agnès Sulem (1)

1 MATHRISK - Mathematical Risk Handling
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 King‘s College London
4 Cornell University [New York]

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.

Mots clés: Dynamic risk measures; BSDE; Mean-field interactions

Domaines: Probabilités [math.PR]

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, inPress, 8 (1), pp.33-52. ⟨10.3934/puqr.2023002⟩. ⟨hal-02421316v2⟩