An appropriate way to switch from the individual risk model to the collective one.

Abstract

For some time now, the convenient and fast calculabdlty of collectwe risk models using the Panjer-algonthm has been a well-known fact, and indeed pracnnoners almost always make use of collective risk models m their dally numerical computanons In doing so, a standard hnk has been preferred for relating such calculations to the underlying heterogeneous risk portfoho and to the approximation of the aggregate claims distribution function m 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 approxlmanon error which arises does not converge to zero ~f the risk portfolio in question continues to grow. Therefore, necessary and sufficient con&nons are derived m order to obtain well-adjusted collectwe risk models which supply convergent approximanons. Moreover, it Is shown how in practical situanons the previous natural hnk between the Individual and the collective risk model can easily be too&fled to improve its calculation accuracy. A numerical example elucidates this