Actuarial Applications in Catastrophe Reinsurance, [Discussion]

Mr. Simon has written an interesting paper which reveals itself to be more a collection of ingenious manipulations of assumed relationships than a set of directions for calculating catastrophe reinsurance premiums. The key sentence is in Section 2. It reads; “Attention will be focused on situations where it will be appropriate to assume that any loss which hits the cover will run all the way through it, that is, all losses will be total losses.” This assumption is not commonly used in catastrophe reinsurance of life portfolios, and I understand that it is not the European practice in non-life catastrophe reinsurance. However, the assumption does have the consequence that the same mathematical results can be obtained by considering one death, two deaths, etc., among a group of lives, each having the same probability of death and the same amount of life insurance. This allows the usual risk theory assumptions of independence, stationary and exclusion of multiple events to be made, so as to permit use of the Poisson distribution to specify the probabilities of a given number of deaths.