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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: eld@codan.dk
Montserrat Guillén
Affiliation:
Dept. Econometrics, RFA-IREA University of Barcelona, Diagonal, 690 08034 Barcelona, Spain E-mail: mguillen@ub.edu
Jim Gustafsson
Affiliation:
Dept. Research & Development, BI SMC Royal & SunAlliance Scandinavia, Gammel Kongevej 60, DK-1790 Copenhagen V, Denmark, E-mail: jgu@codan.dk
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: l.h.nielsen@biostat.ku.dk
Jens Perch Nielsen
Affiliation:
Cass Business School, 106 Bunhill Row, London EC1Y8TE, United Kingdom, E-mail: Jens.Nielsen.1@city.ac.uk
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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.

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