On Duration Effects in Non-Life Insurance Pricing

19 Pages Posted: 18 Jun 2023 Last revised: 25 Oct 2023

Date Written: June 9, 2023

Abstract

The paper discusses duration effects on the consistency of mean parameter and dispersion parameter estimators in exponential dispersion families (EDFs) that are the standard models used for non-life insurance pricing. Focus is on the standard generalised linear model assumptions where both the mean and variance, conditional on duration, are linear functions in terms of duration. We derive simple convergence results that highlight consequences when the linear conditional moment assumptions are not satisfied. These results illustrate that: 1) the resulting mean estimators always have a relevant asymptotic interpretation in terms of the duration adjusted actuarially fair premium – a premium that only agrees with the standard actuarial premium using a duration equal to one, given that the expected value is linear in the duration; 2) deviance based estimators of the dispersion parameter in an EDF should be avoided in favour of Pearson estimators; 3) unless the linear moment assumptions are satisfied consistency of dispersion and plug-in variance estimators can not be guaranteed and may result in spurious over-dispersion.

The results provide explicit conditions on the underlying data generating process that will lead to spurious over-dispersion that can be used used for model checking. This is illustrated based on real insurance data, where it is concluded that the linear moment assumptions are violated, which results in non-negligible spurious over-dispersion.

Keywords: Consistency, Duration, Exponential dispersion family, Generalised linear model, Over-dispersion, Deviance estimators, Pearson estimators

JEL Classification: G22, C18

Suggested Citation

Lindholm, Mathias and Nazar, Taariq, On Duration Effects in Non-Life Insurance Pricing (June 9, 2023). Available at SSRN: https://ssrn.com/abstract=4474908 or http://dx.doi.org/10.2139/ssrn.4474908

Mathias Lindholm (Contact Author)

Stockholm University ( email )

Universitetsvägen 10
Stockholm, Stockholm SE-106 91
Sweden

Taariq Nazar

Stockholm University ( email )

Universitetsvägen 10
Stockholm, Stockholm SE-106 91
Sweden

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