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Document Details : Title: An Appropriate Way to Switch from the Individual Risk to the Collective One Author(s): KUON, S. , RADTKE, M. , REICH, A. Journal: ASTIN Bulletin Volume: 23 Issue: 1 Date: May 1993 Pages: 23-54 DOI: 10.2143/AST.23.1.2005100 Abstract : For some time now, the convenient and fast calculability of collective risk models using the Panjer-algorithm has been a well-known fact, and indeed practitioners almost always make use of collective risk models in their daily numerical computations. In doing so, a standard link has been preferred for relating such calculations to the underlying heterogeneous risk portfolio and to the approximation of the aggregate claims distribution function in the individual risk model. In this procedure until now, the apprommation quality of the collecnve risk model upon which such calculations are based is unknown. It is proved that the approximation error which arises does not converge to zero if the risk portfolio in question continues to grow. Therefore, necessary and sufficient conditons are derived in order to obtain well-adjusted collective risk models which supply convergent approximations. Moreover, it is shown how in practical situations the previous natural link between the Individual and the collective risk model can easily be modified to improve its calculation accuracy. A numerical example elucidates this |
