Abstract This article 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.

中文翻译：

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二分网络中风险过程的破坏概率

摘要 本文通过评估多元复合泊松风险过程的单个和多个组件的破产概率来研究保险市场的风险平衡特征。过程组件的依赖性是由随机二分网络引起的。类比非网络场景，引入网络崩溃参数。这个随机参数取决于二分网络，对破产概率至关重要。在网络上的某些条件下，对于轻尾索赔规模分布，我们获得 Lundberg 界限，对于指数索赔规模分布，我们获得破产概率的准确结果。对于大型稀疏网络，网络破坏参数由独立泊松变量的函数近似。