Sarmanov family of multivariate distributions for bivariate dynamic claim counts model |
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Affiliation: | 1. Department of Software Engineering, Faculty of Computing, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia;2. School Computing and Mathematics, Keele University, Staffordshire, ST5 5BG, UK;1. School of Management, University of Canberra, Bruce, ACT 2601, Australia;2. Department of Marketing, School of Business, Monash University Malaysia Campus, Jalan Legoon Selatan, 46150 Bandar Sunway, Selangor, Malaysia;3. Department of Marketing, Monash University Clayton Campus, Wellington Road, Vic 3800, Australia |
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Abstract: | To predict future claims, it is well-known that the most recent claims are more predictive than older ones. However, classic panel data models for claim counts, such as the multivariate negative binomial distribution, do not put any time weight on past claims. More complex models can be used to consider this property, but often need numerical procedures to estimate parameters. When we want to add a dependence between different claim count types, the task would be even more difficult to handle. In this paper, we propose a bivariate dynamic model for claim counts, where past claims experience of a given claim type is used to better predict the other type of claims. This new bivariate dynamic distribution for claim counts is based on random effects that come from the Sarmanov family of multivariate distributions. To obtain a proper dynamic distribution based on this kind of bivariate priors, an approximation of the posterior distribution of the random effects is proposed. The resulting model can be seen as an extension of the dynamic heterogeneity model described in Bolancé et al. (2007). We apply this model to two samples of data from a major Canadian insurance company, where we show that the proposed model is one of the best models to adjust the data. We also show that the proposed model allows more flexibility in computing predictive premiums because closed-form expressions can be easily derived for the predictive distribution, the moments and the predictive moments. |
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Keywords: | Poisson–Gamma mixture Sarmanov Maximum likelihood estimation A posteriori ratemaking Dynamic claim count |
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