A Comparison: Some Approximations for the Aggregate Claims Distribution

Several approximations for the distribution of aggregate claims have been proposed in the literature. In this paper, we have developed a saddlepoint approximation for the aggregate claims distribution and compared it with some existing approximations, such as NP 2 , gamma, IG, and gamma-IG mixture. Numerical comparisons are made with the exact results, in terms of relative errors, for various combinations of claim count and claim size distributions. The saddlepoint approximation gives very satisfactory accuracy, followed by gamma-IG mixture approximation in all the applications considered in this paper. Address for Correspondence: kthiaga@ilstu.edu