Risk in a large claims insurance market with bipartite graph structure

Journal article

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-atRisk 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 covered by society. In our setting of networks of agents, 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 the risk for society small. We explain the influence of the network structure on diversification effects in different network scenarios.

Authors: Reinert, G; Kley, O; Klueppelberg, C

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: INFORMS (Institute for Operations Research and Management Sciences)
• Journal: Operations Research
• Volume: 64
• Issue: 5
• Pages: 1159 - 1176
• Publication date: 2016-07-22
• Acceptance date: 2016-03-11
• DOI: 10.1287/opre.2016.1502
• EISSN: 1526-5463
• ISSN: 0030-364X
• Keywords: micro- vs. macro-prudential risk; diversification; reinsurance; Pareto-tail; risk measures; multivariate regular variation; Bipartite graph; market risk