Appendix EDiscretization of the Severity Distribution

There are two relatively simple ways to discretize the severity distribution. One is the method of rounding and the other is a mean-preserving method.

E.1 The Method of Rounding

This method has two features: All probabilities are positive and the probabilities add to 1. Let h be the span and let Y be the discretized version of X. If there are no modifications, then

equation

The recursive formula is then used with img. Suppose that a deductible of d, limit of u, and coinsurance of img are to be applied. If the modifications are to be applied before the discretization, then

equation

where img and Z is the modified distribution. This method does not require that the limits be multiples of h, but does require that img be a multiple of h. This method gives the probabilities of payments per payment.

Finally, if there is truncation from above at u, change all denominators ...

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