CAS Monograph No. 8: Stochastic Loss Reserving Using Bayesian MCMC Models (2nd Edition)
by Glenn Meyers, FCAS, MAAA, CERA
The emergence of Bayesian Markov Chain Monte-Carlo (MCMC) models has provided actuaries with an unprecedented flexibility in stochastic model development. Another recent development has been the posting of a database on the CAS website that consists of hundreds of loss development triangles with outcomes. This monograph begins by first testing the performance of the Mack model on incurred data, and the Bootstrap Overdispersed Poisson model on paid data. It then proposes Bayesian MCMC models that improve the performance over the above models. The features examined include (1) recognizing correlation between accident years in incurred data, (2) allowing for a change in the claim settlement rate in paid data, and (3) a unified model combining paid and incurred data. This monograph continues with an investigation of dependencies between lines of insurance and proposes a way to calculate a cost of capital risk margin.
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