Catastrophe Insurance and Solvency Regulation

Abstract

This paper provides a welfare analysis of solvency regulation for catastrophe insurance. We consider an economy with risk-averse agents exposed to a common source of risk and an insurer owned by risk-averse shareholders. We show that the optimal insurance contract features full coverage and is Pareto optimal if and only if it includes participation in the insurer’s profit. When such participation is not available (as is often the case in the real world), we demonstrate that solvency regulation allowing insurer default or limited liability in the most catastrophic states is Pareto improving. We use a numerical application to analyze the welfare benefits of different default rates for a wide range of risk lines, risk correlations, and ratios of insureds to insurer’s shareholders. While allowing a small probability of default yields some welfare gains, we show that an excessive default probability may be highly detrimental to welfare. We find that a good rule of thumb is to maintain a default probability lower than the individual probability of loss.