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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:
91B30Risk theory, insurance
62P05Applications of statistics to actuarial sciences and financial mathematics
62E10Characterization and structure theory of statistical distributions