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

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. For an interacting mean-field particle system with inhomogeneous interactions, we show that the particle system converges to the graphon mean-field BSDE system in some sense. We next 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.