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The Cox Regression Model for Claims Data m Non-Life Insurance

Published online by Cambridge University Press:  29 August 2014

Niels Keiding ,
Christian Andersen  and
Peter Fledelius
Niels Keiding*
Affiliation:
Department of Biostatistics, University of Copenhagen
Christian Andersen*
Affiliation:
ATP PensionService A/S, Hilleroed, Denmark
Peter Fledelius*
Affiliation:
ATP PensionService A/S, Hilleroed, Denmark
*
Institute of Public Health, Department of Biostatistics, University of Copenhagen, 3 Blegdamsvej, DK-2200 Copenhagen N, DenmarkTel. +45 35 32 79 01, Fax, + 45 35 32 79 07
ATP PensionService A/S, Kongens Vaenge 8, DK-3400 Hilleroed, Denmark
ATP PensionService A/S, Kongens Vaenge 8, DK-3400 Hilleroed, Denmark
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Abstract

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The Cox regression model is a standard tool in survival analysis for studying the dependence of a hazard rate on covariates (parametrically) and time (nonparametrically). This paper is a case study intended to indicate possible applications to non-life insurance, particularly occurrence of claims and rating.

We studied individuals from one Danish county holding policies in auto, property and household insurance simultaneously at some point during the four year period 1988-1991 in one company. The hazard of occurrence of claims of each type was studied as function of calendar time, time since the last claim of each type, age of policy holder, urbanization and detailed type of insurance. Particular emphasis was given to the technical advantages and disadvantages (particularly the complicated censoring patterns) of considering the nonparametrically underlying time as either calendar time or time since last claim. In the former case the theory is settled, but the results are somewhat complicated. The latter choice leads to several issues still under active methodological development. We develop a goodness-of-fit criterion which shows the lack of fit of some models, for which the practical conclusions might otherwise have been useful.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 28 , Issue 1 , May 1998 , pp. 95 - 118
Copyright
Copyright © International Actuarial Association 1998

References

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