Tail Conditional Expectations

In modeling catastrophes, it is often useful to know how large a loss can be expected to be, given the assumption that the loss is greater than some amount. This value—the so-called "tail conditional expectation"—may be of great relevance to those who insure or reinsure against the highest levels of losses; it is sometimes what is meant by the actuarial term "probable maximum loss". In this Demonstration, you select a family of distributions and two parameters that instantiate a particular distribution from that family. The resulting distribution determines the probability that a loss from some catastrophe will exceed some amount. You can then set the magnitude of the catastrophe you wish to study. A "return period" of 50, for example, means that you wish to study catastrophes that are larger than all of those that will, on average, occur over a 50 year period. The Demonstration responds by drawing the distribution you have selected (you select whether you want to see the probability density function or the cumulative density function): the red dashed line shows the "exceedance value" and the blue line shows the tail conditional expectation, which is computed using numerical integration. An inset grid recapitulates the results.