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

Risk in a large claims insurance market with bipartite graph structure