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An extension of Panjer’s recursion. (English) Zbl 1098.91540
The paper extends Panjer’s recursion to the Panjer class of order \(k\) for an arbitrary positive integer \(k\). The derivations depend on a differential equation characterizing the probability generating function of a Panjer distribution. These results are of interest in catastrophe excess-of-loss reinsurance.

MSC:
91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
62E10 Characterization and structure theory of statistical distributions
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References:
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