Abstract
In this chapter, we discuss recursive evaluation of compound distributions with counting distribution in the Panjer class and severity distribution on the integers, allowing for negative severities. The cases of binomial, Poisson, and negative binomial counting distribution are treated separately. In the binomial case, the compound distribution can be evaluated exactly when the support of the severity distribution is bounded on at least one side as the support of the counting distribution is bounded from above; otherwise, we truncate the severities and give error bounds for that approximation. For the Poisson and negative binomial cases, we only give approximations; for the negative binomial case, we also give an asymptotic expression.
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