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COMPARING THE DISTRIBUTIONS OF AGGREGATE CLAIMS FOR DIFFERENT PROBABILITY DISTRIBUTIONS UNDER REINSURANCE ARRANGEMENTS
Keywords:
aggregate, claims, distribution, probability, reinsurance.DOI:
https://doi.org/10.17654/0972361722011Abstract
In this study, expressions for estimating the moments of an aggregate payment for a reinsurer have been formulated to guard against the situation of estimating different moments for the aggregate claim data each time a new probability function is used. The formulated aggregate claim distribution of the reinsurer yielded consistent expected value and variance for the amount claimed irrespective of the choice of the probability distribution used to derive the aggregate claim distribution of the reinsurer. Using data simulated from the lognormal distribution (our benchmark distribution), we found that for the expectation and variance of the aggregate payment distribution of the reinsurer, when the losses were assumed to be from the gamma and Pareto distributions, were not significantly different from that of our benchmark distribution. Given losses with very small variance, the beta distribution and the benchmark distribution produced consistent estimates for the expectation of the aggregate payment distribution for the reinsurer which was not significantly different from that of the gamma distribution. However, given claim data with extremely large variance, the gamma and Pareto distributions performed at least as well as the lognormal distribution in estimating expectation and variance of the aggregate claim.
Received: November 18, 2021
Accepted: January 11, 2022
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