Graphon Mean-Field Backward Stochastic Differential Equations With Jumps and Associated Dynamic Risk Measures

Abstract

We study graphon mean-field backward stochastic differential equations (BSDEs) with jumps and associated dynamic risk measures. We establish the existence, uniqueness and measurability of solutions under some regularity assumptions and provide some estimates for the solutions.
We moreover prove the stability with respect to an interacting graphon particle systems,
and obtain the convergence of an interacting mean-field particle system with inhomogeneous interactions to the graphon mean-field BSDE.
We then provide some comparison theorems for the graphon mean-field BSDEs. As an application, we introduce the graphon dynamic risk measure induced by the solution of a graphon mean-field BSDE system and study its properties. We finally provide a dual representation theorem for the graphon dynamic risk measure in the convex case.

Keywords: Mean-field BSDEs with jumps, graphon particle systems, dynamic risk measures

JEL Classification: C02