Cascading Losses in Reinsurance Networks

TL;DR

This paper introduces a comprehensive model for contagion in reinsurance networks, revealing significant underestimation of risks by simpler models and highlighting the importance of nonlinearities and network structure in risk assessment.

Contribution

The paper develops a general contagion model for reinsurance networks, characterizes its fixed points, and provides efficient algorithms with convergence guarantees, advancing understanding of complex network effects.

Findings

Reinsurance networks are highly sensitive to parameter changes.

Small fraud cases can significantly impact overall losses.

Nonlinear contracts can obscure risks and increase costs.

Abstract

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. We lastly 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, as 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.