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Sensitivity analysis of the moments of the profit on an Income Protection Policy

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  • Isabel Maria Cordeiro
  • Pedro Manuel Magalhães

Abstract

The main purpose of this paper is to perform a sensitivity analysis where we quantify and analyse the effects on the mean of the profit on an Income Protection policy and two risk measures of changing the values of the transition intensities. All the calculations carried out are based on a multiple state model for Income Protection proposed in Continuous Mortality Investigation Committee (Continuous Mortality Investigation Reports 1991; 12). Within this model, we derive a formula for the mean of the profit, which enables to evaluate it more efficiently. In order to calculate the two risk measures we use the numerical algorithms for the calculation of the moments of the profit proposed by Waters (Insurance: Mathematics and Economics 1990; 9:101–113). We carry out the sensitivity analysis considering two different situations: in the first situation, we update the premium rates used to calculate the moments of the profit, according to the changes in the values of the transition intensities; in the second one, we do not update the premium rates. Both analyses are of practical interest to insurance companies selling Income Protection policies. Copyright © 2009 John Wiley & Sons, Ltd.

Suggested Citation

  • Isabel Maria Cordeiro & Pedro Manuel Magalhães, 2010. "Sensitivity analysis of the moments of the profit on an Income Protection Policy," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(1), pages 50-70, January.
    • Handle: RePEc:wly:apsmbi:v:26:y:2010:i:1:p:50-70
    DOI: 10.1002/asmb.766
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    References listed on IDEAS

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    1. Waters, Howard, 1990. "The recursive calculation of the moments of the profit on a sickness insurance policy," Insurance: Mathematics and Economics, Elsevier, vol. 9(2-3), pages 101-113, September.
    2. Cordeiro, Isabel Maria Ferraz, 2002. "A multiple state model for the analysis of permanent health insurance claims by cause of disability," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 167-186, April.
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