Peters, GW; Dong, AXD; Kohn, R; (2014) A copula based Bayesian approach for paid-incurred claims models for non-life insurance reserving. Insurance: Mathematics and Economics , 59 pp. 258-278. 10.1016/j.insmatheco.2014.09.011.

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Abstract

Our article considers the class of recently developed stochastic models that combine claims payments and incurred losses information into a coherent reserving methodology. In particular, we develop a family of hierarchical Bayesian paid-incurred claims models, combining the claims reserving models of Hertig (1985) and Gogol (1993). In the process we extend the independent log-normal model of Merz and Wüthrich (2010) by incorporating different dependence structures using a Data-Augmented mixture Copula paid-incurred claims model.In this way the paper makes two main contributions: firstly we develop an extended class of model structures for the paid-incurred chain ladder models where we develop precisely the Bayesian formulation of such models; secondly we explain how to develop advanced Markov chain Monte Carlo sampling algorithms to make inference under these copula dependence PIC models accurately and efficiently, making such models accessible to practitioners to explore their suitability in practice. In this regard the focus of the paper should be considered in two parts, firstly development of Bayesian PIC models for general dependence structures with specialised properties relating to conjugacy and consistency of tail dependence across the development years and accident years and between Payment and incurred loss data are developed. The second main contribution is the development of techniques that allow general audiences to efficiently work with such Bayesian models to make inference. The focus of the paper is not so much to illustrate that the PIC paper is a good class of models for a particular data set, the suitability of such PIC type models is discussed in Merz and Wüthrich (2010) and Happ and Wüthrich (2013). Instead we develop generalised model classes for the PIC family of Bayesian models and in addition provide advanced Monte Carlo methods for inference that practitioners may utilise with confidence in their efficiency and validity.

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