Insurance loss distributions are characterized by a high frequency of small amounts and a lower, but the not insignificant, occurrence of large claim amounts. Composite models, which link two probability distributions, one for the “belly” and the other for the “tail” of the loss distribution, have emerged in the actuarial literature to take this specificity into account. The parameters of these models summarize the distribution of the losses. One of them corresponds to the breaking point between small and large claim amounts. The composite models are usually fitted using maximum likelihood estimation. A Bayesian approach is considered in this work. Sequential Monte Carlo samplers are used to sample from the posterior distribution and compute the posterior model evidence to both fits and compare the competing models. The method is validated via a simulation study and illustrated on insurance loss datasets.
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Pierre-O. Goffard is an associate professor at l’Institut de Science Financière et d’Assurances a graduate school specialized in actuarial science part of the University Claude Bernard Lyon 1. His research interest lies at the intersection of probability and statistics applied to risk theory, claim modeling, and blockchain analysis.