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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:
 [1] Mitt. Verein. Schweiz. Versicherungsmathematiker 85 pp 157– (1985) [2] Univariate Discrete Distributions (1992) [3] Mitt. Verein. Schweiz. Versicherungsmathematiker 55 pp 499– (1955) [4] Scand. Actuar. J. pp 117– (1986) [5] Lundberg Approximations for Compound Distributions with Insurance Applications (2001) [6] Loss Models (1998) [7] DOI: 10.2143/AST.22.1.2005127 · doi:10.2143/AST.22.1.2005127 [8] ASTIN Bull. 12 pp 27– (1981) · doi:10.1017/S0515036100006802 [9] Versicherungsmathematik (2001) · JFM 54.0573.16 [10] Lectures on Risk Theory (1996) · Zbl 0847.60002 [11] ASTIN Bull 12 pp 22– (1981) · doi:10.1017/S0515036100006796 [12] DOI: 10.2143/AST.18.1.2014957 · doi:10.2143/AST.18.1.2014957
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