Strategies for offering an m-out-of-n policy for multi-peril catastrophe insurance

A company with n geographically widely dispersed sites seeks an insurance policy that pays off if m out of the n sites experience rarely occurring catastrophes (e.g., earthquakes) during a year. This study compares three strategies for an insurance company wishing to offer such an m -out-of- n policy, assuming the existence of markets for insurance on the individual sites with coverage periods of various lengths of a year or less. Strategy A is static: at the beginning of the year it buys a reinsurance policy on each individual site covering the entire year and makes no later adjustments. By contrast, Strategies S and C are dynamic and adaptive, exploiting the availability of individual-site policies for shorter periods than a year to make changes in the coverage on individual sites as quakes occur during the year. Strategy S uses the payoff from reinsurance when a quake occurs at a particular site to increase coverage for the remainder of the year on the sites that have not yet had quakes. Strategy C buys individual-site policies covering successive time periods of fixed length, observing the system at the beginning of each period and using cash on hand plus cash obtained from a reinsurance payoff (if any) during the previous period to decide how much cash to retain and how much reinsurance to purchase for the current period. The study relies on expected utility to determine indifference premiums and compare the premiums and loss probabilities for the three strategies.