  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.
