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Multivariate Latent Risk: A Credibility Approach

Published online by Cambridge University Press:  17 April 2015

Martin Englund ,
Montserrat Guillén ,
Jim Gustafsson ,
Lars Hougaard Nielsen  and
Jens Perch Nielsen
Martin Englund
Affiliation:
Dept. Research & Development, BI SMC Royal & SunAlliance Scandinavia, Gammel Kongevej 60, DK-1790 Copenhagen V, Denmark, E-mail: [email protected]
Montserrat Guillén
Affiliation:
Dept. Econometrics, RFA-IREA University of Barcelona, Diagonal, 690 08034 Barcelona, Spain E-mail: [email protected]
Jim Gustafsson
Affiliation:
Dept. Research & Development, BI SMC Royal & SunAlliance Scandinavia, Gammel Kongevej 60, DK-1790 Copenhagen V, Denmark, E-mail: [email protected]
Lars Hougaard Nielsen
Affiliation:
Dept. Biostatistics, Institute of Public Health University of Copenhagen, Øster Farimagsgade 5B, P.O.Box 20299, DK-1014 Copenhagen K, Denmark, E-mail: [email protected]
Jens Perch Nielsen
Affiliation:
Cass Business School, 106 Bunhill Row, London EC1Y8TE, United Kingdom, E-mail: [email protected]
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Abstract

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We investigate a concept of multivariate pricing, which includes claim history for more than one line of business and is a generalization of the Bühlmann-Straub model. The multivariate credibility model is extended to allow for the age of claims to influence the estimation of future claims. The model is applied to data from a portfolio of commercial lines of business.

Keywords

Bonus-Malus SystemMultivariate CredibilityTime-dependent Random Effects
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 38 , Issue 1 , May 2008 , pp. 137 - 146
Copyright
Copyright © ASTIN Bulletin 2008

Footnotes

1

University of Aarhus and Royal & SunAlliance, Denmark.

2

University of Barcelona, Spain. Thanks are given to the Spanish Ministerio de Educacion y Ciencia, FEDER grant SEJ2007-63298.

3

University of Copenhagen and Royal & SunAlliance, Denmark.

4

University of Copenhagen, Denmark.

5

Cass Business School, City University, United Kingdom.

All authors would like to thank two anonymous referees whom kindly suggested many improvements to an earlier draft.

References

Bichsel, F. (1967) Experience rating in subsets of risks. ASTIN Bulletin, 4, 210–227.CrossRefGoogle Scholar
Bühlmann, H. (1967) Experience rating and credibility. ASTIN Bulletin, 4, 199–207.CrossRefGoogle Scholar
Bühlmann, H. and Gisler, A. (2005) A course in credibility theory and its applications. Springer-Verlag, Heidelberg.Google Scholar
Bühlmann, H., Gisler, A. and Kollöffel, D. (2003) Multidimensional credibility applied to estimating the frequency of big claims. http://www.astin2003.de/img/papers/gisler.pdf Google Scholar
Desjardins, D., Dionne, G. and Pinquet, J. (2001) Experience rating schemes for fleets of vehicles. ASTIN Bulletin, 31, 81–105.CrossRefGoogle Scholar
Dionne, G. and Vanasse, C. (1992) Automobile insurance ratemaking in the presence of asymmetrical information. Journal of Applied Econometrics, 7(2), 149–165.CrossRefGoogle Scholar
Gerber, H.U. and Jones, D.A. (1975) Credibility Formulas of the Updating Type. Transaction of the Society of Actuaries, 27, 31–52.Google Scholar
Gouriéroux, C., Monfort, A. and Trognon, A. (1984) Pseudo maximum likelihood methods: applications to Poisson models. Econometrica, 52, 701–720.CrossRefGoogle Scholar
Jewell, W.S. (1973) Multidimensional Credibility. Operations Research Center 73–7, Berkeley.Google Scholar
Jewell, W.S. (1974) Exact multidimensional credibility. Bulletin of Swiss Association of Actuaries, 74, 193–214.Google Scholar
Lemaire, J. (1995) Bonus-Malus Systems in Automobile Insurance. Kluwer Academic Publishers, Boston.CrossRefGoogle Scholar
Lundberg, O. (1966) Une note sur des systèmes de tarification basés sur des modèles du type Poisson composé, ASTIN Bulletin, 4, 49–58.CrossRefGoogle Scholar
Lütkepohl, H. (2005) New Introduction to Multiple Time Series Analysis, Springer Verlag, Heidelberg.CrossRefGoogle Scholar
Mccullagh, P. and Nelder, J.A. (1989) Generalized Linear Models, no. 37 in Monograph on Statistics and Applied Probability, Chapman & Hall, Cambridge, 2nd ed.Google Scholar
Norberg, R. (2004) Credibility theory. In Encyclopaedia of Actuarial Science (ed. Sundt, B. and Teugels, J.), Wiley, New York.Google Scholar
Pinquet, J. (1997) Allowance for the cost of claims in Bonus-Malus systems. ASTIN Bulletin, 27, 33–57.CrossRefGoogle Scholar
Pinquet, J. (1998) Designing optimal Bonus-Malus system from different types of claims. ASTIN Bulletin, 28, 205–220.CrossRefGoogle 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
Sundt, B. (1981) Recursive credibility estimation. Scandinavian Actuarial Journal, 3–21.CrossRefGoogle Scholar