Robustness in Bayesian Models for Bonus–Malus Systems

E. Gómez-Déniz and F. J. Vázquez-Polo
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E. Gómez-Déniz: Department of Metodos Cuantitativos en Economia y Gestion, Titular de Universidad, Campus Universitario de Tafira, 35017 Las Palmas de Gran, Canaria, Spain
F. J. Vázquez-Polo: Department of Quantitative Methods, University of Las Palmas de G.C., Campus Universitario de Tafira, 35017 Las Palmas de Gran Canaria, Spain

Chapter 12 in Intelligent and Other Computational Techniques in Insurance:Theory and Applications, 2003, pp 435-463 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractIn implementing Bayesian models for a Bonus–Malus System (BMS) it is normal to include a parametric structure, π0(λ), in the insurer's portfolio. According to Bayesian sensitivity analysis, the structure function can be modelled by specifying a class Γ of priors instead of a single prior. In this chapter, we examine the ranges of the relativities, i.e., δπ = 𝔼 [λπ(λ | data)]/𝔼[λπ(λ)], π ∈ Γ. We combine standard and robust Bayesian tools to show how the choice of the prior can critically affect the relative premiums. Extending the recent paper of Gómez et al. (2002b), we develop our model to the Negative Binomial–Pareto model (Meng and Whitmore 1999) and the Poisson–Inverse Gaussian model (Tremblay 1992, Besson and Partrat 1992) and also extend the class of prior densities to ones that are more realistic in the actuarial setting, i.e., the classes of generalized moments conditions. We illustrate our method with data from Lemaire (1979). The chapter is mainly focused on showing that there exists an appropriate methodology to develop a Bayesian sensitivity analysis of the bonus-malus of loaded premiums.

Keywords: Insurance; Actuarial Science; Neural Networks; Fuzzy Systems; Computational Intelligence; Computational Techniques; Life and Health Insurance; Property and Casualty Insurance (search for similar items in EconPapers)
Date: 2003
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