Abstract

Journal of Actuarial Practice

Volume 7, Numbers 1 and 2, 1999


A Saddlepoint Approximation for Tail Probabilities in Collective Risk Models

Dale Borowiak

Abstract

Collective risk models are often used to model the aggregate claims generated in a fixed time from  a portfolio or group of insurance policies. As the aggregate claims form a compound random variable, it is usually difficult to work with its distribution. Actuaries have used several different types of approximations of this distribution. The objective of this paper is to introduce actuaries to a more robust method of approximating tail probabilities: the saddlepoint approximation.  This approximation is applied to specific cases that include heavy tailed distributions. The approximation is compared to the exact calculations.

Key words and phrases: moment-generating function, aggregate claims distribution, heavy tail.

Dale Borowiak

Department of Statistics

University of Akron,

308 Buchtel Common,

Akron OH 44325-1913


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