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The effect of model uncertainty on the pricing of critical illness insurance

Published online by Cambridge University Press:  23 October 2014

Erengul (Ozkok) Dodd ,
George Streftaris ,
Howard R. Waters  and
Andrew D. Stott
Erengul (Ozkok) Dodd*
Affiliation:
Southampton Statistical Sciences Research Institute and Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ, UK
George Streftaris
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh, EH14 4AS, UK
Howard R. Waters
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh, EH14 4AS, UK
Andrew D. Stott
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh, EH14 4AS, UK
*
*Correspondence to: Erengul Dodd, Southampton Statistical Sciences Research Institute and Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ, UK. Tel: 0044 238059 3679; E-mail: [email protected]
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Abstract

In this paper we calculate and compare diagnosis and net premium rates for critical illness insurance using different models for the claim delay distribution (CDD). The choice of CDD affects the diagnosis rates and hence the net premium rates in two ways: through the estimation of missing dates of diagnosis and through the adjustment of the exposure to allow for claims diagnosed but not settled in the observation period. We consider two CDDs: a three-parameter Burr distribution and a lognormal distribution. Our conclusion, based on a single, but extensive, data set, is that net premium rates are not significantly affected by the choice of CDD.

Keywords

Critical illness insuranceClaim delay distributionStatistical modellingDiagnosis ratesPricing
Type
Papers
Information
Annals of Actuarial Science , Volume 9 , Issue 1 , March 2015 , pp. 108 - 133
Copyright
© Institute and Faculty of Actuaries 2014 

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References

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