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Document Details :

Title: An Evolutionary Credibility Model for Claim Numbers
Author(s): ALBRECHT, Peter
Journal: ASTIN Bulletin
Volume: 15    Issue: 1   Date: April 1985   
Pages: 1-17
DOI: 10.2143/AST.15.1.2015029

Abstract :
This paper considers a particular credibility model for the claim numbers Ni, N2,..., Nn,... of a single risk within a collective in successive periods 1, 2,..., n, .... In the terminology of Jewell (1975) the model Is an evolutionary credibility model, which means that the underlying risk parameter A is allowed to vary in successive periods (the structure function is allowed to be time dependent). Evolutionary credibility models for claim amounts have been studied by B├╝hlmann (1969, pp. 164-165), Gerber and Jones (1975), Jewell (1975, 1976), Taylor (1975), Sundt (1979, 1981, 1983) and Kremer (1982). Again in Jewell's terminology the considered model is on the other hand stationary, in the sense that the conditional distribution of N, given the underlying risk parameter does not vary with i.