Comparison: Some Approximations for the Aggregate Claims Distribution
By Ranee Thiagarajah
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 NP2, 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 satis-factory accuracy, followed by gamma-IG mixture approximation in all the applications considered in this paper.
Keywords Frequency distribution, severity distribution, aggregate claims distribution, approximation methods