Can Insurers Pay for the "Big One"? Measuring the Capacity of an Insurance Market to Respond to Catastrophic Losses

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Abstract
This paper presents a theoretical and empirical analysis of the capacity of the U.S. property-liability insurance industry to finance major catastrophic property losses. The topic is important because catastrophic events such as the Northridge earthquake and Hurricane Andrew have raised questions about the ability of the insurance industry to respond to the "Big One," usually defined as a hurricane or earthquake in the $100 billion range. At first glance, the U.S. property-liability insurance industry, with equity capital of more than $300 billion, should be able to sustain a loss of this magnitude. However, the reality could be different; depending on the distribution of damage and the spread of coverage as well as the correlations between insurer losses and industry losses. Thus, the prospect of a mega catastrophe brings the real threat of widespread insurance failures and unpaid insurance claims. Our theoretical analysis takes as its starting point the well-known article by Borch (1962), which shows that the Pareto optimal result in a market characterized by risk averse insurers is for each insurer to hold a proportion of the "market portfolio" of insurance contracts. Each insurer pays a proportion of total industry losses; and the industry behaves as a single firm, paying 100 percent of losses up to the point where industry net premiums and equity are exhausted. Borch's theorem gives rise to a natural definition of industry capacity as the amount of industry resources that are deliverable conditional on an industry loss of a given size. In our theoretical analysis, we show that the necessary condition for industry capacity to be maximized is that all insurers hold a proportionate share of the industry underwriting portfolio. The sufficient condition for capacity maximization, given a level of total resources in the industry, is for all insurers to hold a net of reinsurance underwriting portfolio which is perfectly correlated with aggregate in
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