Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-25T15:48:46.346Z Has data issue: false hasContentIssue false
  • English
  • Français

Dependence in Dynamic Claim Frequency Credibility Models

Published online by Cambridge University Press:  17 April 2015

Oana Purcaru  and
Michel Denuit
Oana Purcaru
Affiliation:
Institut de Statistique & Institut des Sciences Actuarielles, Université Catholique de Louvain, Voie du Roman Pays, 20 B-1348 Louvain-la-Neuve, Belgium, E-mail: purcaru@stat.ucl.ac.be & denuit@stat.ucl.ac.be
Michel Denuit
Affiliation:
Institut de Statistique & Institut des Sciences Actuarielles, Université Catholique de Louvain, Voie du Roman Pays, 20 B-1348 Louvain-la-Neuve, Belgium, E-mail: purcaru@stat.ucl.ac.be & denuit@stat.ucl.ac.be
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In nonlife insurance, actuaries usually resort to random effects to take unexplained heterogeneity into account (in the spirit of the Bühlmann-Straub model). This paper aims to study the kind of dependence induced by the introduction of correlated latent variables in the annual numbers of claims reported by policyholders. The effect of reporting claims on the a posteriori distribution of the random effects will be made precise. This will be done by establishing some stochastic monotonicity property of the a posteriori distribution with respect to the claims history.

Keywords

Poisson mixturecredibility theoryexperience ratingrisk classificationcopulastime series for non-gaussian responses
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 33 , Issue 1 , May 2003 , pp. 23 - 40
Copyright
Copyright © ASTIN Bulletin 2003

References

Barlow, R.E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing – Probability Models. Holt, Rinehart and Winston.Google Scholar
Bühlmann, H. (1967) Experience rating and credibility. ASTIN Bulletin 4, 199–207.CrossRefGoogle Scholar
Bühlmann, H. (1970) Mathematical Methods in Risk Theory. Springer Verlag, New York.Google Scholar
Dionne, G. and Vanasse, C. (1989) A generalization of actuarial automobile insurance rating models: the Negative Binomial distribution with a regression component. ASTIN Bulletin 19, 199–212.10.2143/AST.19.2.2014909CrossRefGoogle Scholar
Frees, E.W. and Valdez, E.A. (1998) Understanding relationships using copulas. North American Actuarial Journal 2, 1–15.CrossRefGoogle Scholar
Fahmy, S., Pereira, C.A., Proschan, F. and Shaked, M. (1982) The influence of the sample on the posterior distribution. Communications in Statistics – Theory & Methods 11, 1157–1168.CrossRefGoogle Scholar
Gerber, H.U. and Jones, D. (1975) Credibility formulas of the updating type. Transactions of the Society of Actuaries 27, 31–52.Google Scholar
Joe, H. (1997) Multivariate Models and Dependence Concepts. Chapman & Hall, London.Google Scholar
Kaas, R., Van Heerwaarden, A.E. and Goovaerts, M.J. (1994) Ordering of Actuarial Risks. CAIRE. Brussels.Google Scholar
Kemperman, J.H.B. (1977) On the FKG-inequality for measures on a partially ordered space. Indagationes Mathematicae 39, 313–331.CrossRefGoogle Scholar
Pinquet, J. (2000) Experience rating through heterogeneous models. In Handbook of Insurance, edited by Dionne., G. Kluwer Academic Publishers.Google Scholar
Pinquet, J., Guillén, M. and Bolancé, C. (2001) Allowance for the age of claims in bonus-malus systems. ASTIN Bulletin 31, 337–348.CrossRefGoogle Scholar
Pitt, L.D. (1982) Positively correlated normal variables are associated. The Annals of Probability 10, 496–499.CrossRefGoogle Scholar
Purcaru, O. and Denuit, M. (2002) On the dependence induced by frequency credibility models. Belgian Actuarial Bulletin 2, 74–80.Google Scholar
Renshaw, A.E. (1994) Modelling the claim process in the presence of covariates. ASTIN Bulletin 24, 265–285.CrossRefGoogle Scholar
Shaked, M. and Shanthikumar, J.G. (1994) Stochastic Orders and Their Applications. Academic Press, New York.Google Scholar
Shaked, M. and Spizzichino, F. (1998) Positive dependence properties of conditionally independent random lifetimes. Mathematics of Operations Research 23, 944-959.CrossRefGoogle Scholar
Sundt, B. (1988) Credibility estimators with geometric weights. Insurance: Mathematics and Economics 7, 113–122.Google Scholar
Tong, Y.L. (1990) The Multivariate Normal Distribution. Springer-Verlag, New York.CrossRefGoogle Scholar
Whitt, W. (1979) A note on the influence of the sample on the posterior distribution. Journal of the American Statistical Association 74, 424–426.Google Scholar