IMPROVED APPROXIMATIONS FOR THE AGGREGATE CLAIMS DISTRIBUTION IN THE INDIV IDUAL MODEL

Kornya-type higher order approximations are derived for the aggregate claims distribution and for stop loss premiums in the individual model with arbitrary positive claims. Absolute error bounds and error bounds based on concentration functions are given. In the Gerber portfolio containing 31 policies, second order approximations lead to an accuracy of 3 x 10-4, and third order approximations to 1.7xl0-5. KEYWORDS Aggregate claims distributiori, compound Poisson distribution, approximations. higher order I. INTRODUCTION AND SUMMARY Consider a portfolio containing N policies, where for i = l,..., N the claim amounts distribution Q ~ of the individual risk i can be represented as Q, = (l- q;)8o+ q,P;