Conditional risk measures in a bipartite market structure

In this paper we study the effect of network structure between agents and objects on measures for systemic risk. We model the influence of sharing large exogeneous losses to the financial or (re)insuance market by a bipartite graph. Using Pareto-tailed losses and multivariate regular variation we obtain asymptotic results for systemic conditional risk measures based on the Value-at-Risk and the Conditional Tail Expectation. These results allow us to assess the influence of an individual institution on the systemic or market risk and vice versa through a collection of conditional systemic risk measures. For large markets Poisson approximations of the relevant constants are provided in the example of an insurance market. The example of an underlying homogeneous random graph is analysed in detail, and the results are illustrated through simulations.