Commentary on "Should the government provide insurance for catastrophes?"

insurance liabilities and the stochastic processes generating losses. It is assumed the insurer collects premiums at the beginning of the period equal to the expected loss. Capital is therefore required to cover the actual losses in excess of the expected value. The computations are basically applications of the law of large numbers and the central limit theorem. Cummins assumes a normal distribution, although he properly states that comparable results are available for a wider range of distributions. Cummins shows that, when the risks are identically and independently distributed (i.i.d.), the required capital per policy approaches zero as the number of individual policies approaches infinity. In contrast, when the risks are correlated, some amount of capital is required even in the limit as the number of risks approaches infinity. Cummins reasonably interprets this as meaning that catastrophic risks, which sensibly imply correlated risks, require more capital than do independent risks. I think it important to add that fat-tailed distributions raise an even more distinctive issue, which may help explain why most catastrophe insurance lines are generally not offered by private insurers. A key property of fat-tailed distributions is that the benefits of diversification may not arise. For example, let an insurer start with a portfolio consisting of just one catastrophic risk, say risk A. Now suppose the insurer decides to diversify by creating a portfolio with one-half risk A and one-half risk B. Remarkably, the risk exposure of the portfolio may actually rise, contrary to the normal case of diversification benefits. The intuAGENDA F irst, the conference planners must be complemented for their foresight to put catastrophe insurance on the agenda for this conference, long before Hurricane Katrina crashed into New Orleans. As Katrina illustrates, the problems affecting catastrophe insurance in the United States are taking on, well, catastrophic proportions. Major changes are required in how the government intervenes in each of the major catastrophic risks—earthquakes, floods, hurricanes, and terrorism. Turning to the task at hand, it is always a pleasure and enlightening to read a paper by David Cummins (2006). This one is no exception. My comments follow the lines of David’s paper, taking up these topics in turn:

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