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Bayesian Chain Ladder Models

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Bayesian Claims Reserving Methods in Non-life Insurance with Stan

Abstract

We study the Bayesian chain ladder models and their extensions in this chapter. In Sect. 4.1, the non-life insurance claims reserving background is reviewed. There are two parts in this section. The first part reviews claims reserving terminology. The second part summarizes widely used traditional reserving methods, including the chain ladder (CL) method and the Bornhuetter-Ferguson (BF) method. Stochastic models are discussed in Sects. 4.2 and 4.3. We focus on a Bayesian over-dispersed Poisson (ODP) model with an exponential decay curve component (Verrall et al. 2012). Reversible jump MCMC is used to simulate a sample from this model. In Sect. 4.4, we propose a compound model based on the payments per claim incurred (PPCI) method. A fully Bayesian analysis blending with preliminary classical model checking is performed on the weekly benefit data set and the doctor benefit data set from WorkSafe Victoria, a workers compensation scheme in Victoria state of Australia. We compare our results with the PwC evaluation (Simpson and McCourt 2012) .

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Authors and Affiliations

  1. School of Statistics, Renmin University of China, Beijing, China

    Guangyuan Gao

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  1. Guangyuan Gao
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Correspondence to Guangyuan Gao .

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Gao, G. (2018). Bayesian Chain Ladder Models. In: Bayesian Claims Reserving Methods in Non-life Insurance with Stan. Springer, Singapore. https://doi.org/10.1007/978-981-13-3609-6_4

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