Comparison: Some Approximations for the Aggregate Claims Distribution

By Ranee Thiagarajah

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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


Thiagarajah, Ranee, "Comparison: Some Approximations for the Aggregate Claims Distribution," Variance 13:2, 2021, pp. 190-206.

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Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.