Cascading Losses in Reinsurance Networks
研究了再保险网络中损失通过合同传染的模型，发现简单比例再保险严重低估风险，并揭示了参数敏感性和非线性合同对系统损失的放大效应。
We develop a model for contagion in reinsurance networks by which primary insurers’ losses are spread through the network. Our model handles general reinsurance contracts, such as typical excess of loss contracts. We show that simpler models existing in the literature—namely proportional reinsurance—greatly underestimate contagion risk. We characterize the fixed points of our model and develop efficient algorithms to compute contagion with guarantees on convergence and speed under conditions on network structure. We characterize exotic cases of problematic graph structure and nonlinearities, which cause network effects to dominate the overall payments in the system. Last, we apply our model to data on real-world reinsurance networks. Our simulations demonstrate the following. (1) Reinsurance networks face extreme sensitivity to parameters. A firm can be wildly uncertain about its losses even under small network uncertainty. (2) Our sensitivity results reveal a new incentive for firms to cooperate to prevent fraud, because even small cases of fraud can have outsized effect on the losses across the network. (3) Nonlinearities from excess of loss contracts obfuscate risks and can cause excess costs in a real-world system. This paper was accepted by Baris Ata, stochastic models and simulation.