Catastrophe Risk-Sharing Decisions of Individuals, Insurer, and Government

Abstract

We develop a dynamic game model for efficient catastrophe risk-sharing that allows decision makers to derive optimal pricing, capital, and buying decisions in one equilibrium. Existing catastrophe insurance models focus on either the primary insurance market or the reinsurance market, thus involving one or two decision makers. Our model involves both markets and three decision makers: Individuals, a private insurer, and a centralized agency acting as reinsurer. We show that government reinsurance addresses the failure of the private catastrophe insurance market, increases individuals’ willingness to pay for catastrophe risk transfer, and represents a Pareto improvement on a competitive market with no reinsurance or with private reinsurance. The government’s trade-off between using catastrophe taxes and reinsurance premiums to fund the program improves the social welfare through product quality, capital cost, and wealth transfer channels. Furthermore, a government reinsurance program is a complement to an ex-post catastrophe-relief program and a risk-based solvency regulation.