Paul Krugman has written a nice piece explaining the "death spiral" problem in the insurance business. He said:
Bear in mind that private health insurance only works if insurers can sell policies to both sick and healthy customers. If too many healthy people decide that they’d rather take their chances and remain uninsured, the risk pool deteriorates, forcing insurers to raise premiums. This, in turn, leads more healthy people to drop coverage, worsening the risk pool even further, and so on.
The background is the teetering state of some private health insurers in California.
Chapter 3 of Numbers Rule Your World addresses this problem, using Florida hurricane insurers as an example. Statistics is behind the entire concept of insurance. With large numbers of customers, insurance firms can predict their annual losses (i.e. payouts) with a high degree of certainty. This is a result of the law of large numbers. Because individuals, especially when young, will have difficulty predicting when, and how, they will die, they have an incentive to buy insurance.
But hurricane insurance, or more broadly, disaster insurance, firms face even thornier issues than health insurers. Health insurers can reliably predict and control what proportion of their customer base will get sick each year. What about hurricane insurers? For them, "healthy customers" are analogous to residents with homes in areas that are not hurricane-prone; do we think they are carrying hurricane insurance?
PS. For the economists out there, the question being tossed around is: are hurricane risks insurable? can a private market for hurricane insurance survive?