Mean Field BSDEs and Global Dynamic Risk Measures

We study Mean-field BSDEs with jumps and a generalized mean-field operator that can capture higher order interactions such as those occurring on an inhomogeneous random graph. We provide comparison and strict comparison results. Based on these, we interpret the BSDE solution as a global dynamic risk measure that can account for the intensity of system interactions and therefore incorporate systemic risk. Using Fenchel-Legendre transforms, we establish a dual representation for the risk measure, and in particular we exhibit its dependence on the mean-field operator