Risk in a large claims insurance market with bipartite graph structure

TL;DR

This paper models the impact of network structure on risk measures in a large claims insurance market with Pareto-tailed losses, revealing how diversification strategies depend on tail heaviness and network connectivity.

Contribution

It introduces a bipartite graph model to analyze the influence of network structure on risk measures like VaR and CVaR in heavy-tailed insurance claims, providing new asymptotic results.

Findings

Network structure significantly affects tail risk measures.

Diversification benefits depend on Pareto tail exponent.

Uninsured losses are influenced by network connectivity.

Abstract

We model the influence of sharing large exogeneous losses to the reinsurance market by a bipartite graph. Using Pareto-tailed claims and multivariate regular variation we obtain asymptotic results for the Value-at-Risk and the Conditional Tail Expectation. We show that the dependence on the network structure plays a fundamental role in their asymptotic behaviour. As is well-known in a non-network setting, if the Pareto exponent is larger than 1, then for the individual agent (reinsurance company) diversification is beneficial, whereas when it is less than 1, concentration on a few objects is the better strategy. An additional aspect of this paper is the amount of uninsured losses which have to be convered by society. In the situation of networks of agents, in our setting diversification is never detrimental concerning the amount of uninsured losses. If the Pareto-tailed claims have finite mean, diversification turns out to be never detrimental, both for society and for individual agents. In contrast, if the Pareto-tailed claims have infinite mean, a conflicting situation may arise between the incentives of individual agents and the interest of some regulator to keep risk for society small. We explain the influence of the network structure on diversification effects in different network scenarios.