Ruin probabilities for risk processes in a bipartite network

TL;DR

This paper analyzes ruin probabilities in a multivariate risk process influenced by a bipartite network, introducing a network ruin parameter that captures dependence and allows for bounds and exact calculations under specific conditions.

Contribution

It introduces a novel network ruin parameter for risk processes on bipartite networks, providing bounds and exact ruin probabilities for certain claim distributions.

Findings

Derived Lundberg bounds for ruin probabilities.

Obtained exact ruin probabilities for exponential claim sizes.

Approximated the ruin parameter for large sparse networks.

Abstract

This paper studies risk balancing features in an insurance market by evaluating ruin probabilities for single and multiple components of a multivariate compound Poisson risk process. The dependence of the components of the process is induced by a random bipartite network. In analogy with the non-network scenario, a network ruin parameter is introduced. This random parameter, which depends on the bipartite network, is crucial for the ruin probabilities. Under certain conditions on the network and for light-tailed claim size distributions we obtain Lundberg bounds and, for exponential claim size distributions, exact results for the ruin probabilities. For large sparse networks, the network ruin parameter is approximated by a function of independent Poisson variables. T