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A health insurance pricing model based on prevalence rates: Application to critical illness insurance

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  • Baione, Fabio
  • Levantesi, Susanna

Abstract

The Italian health insurance market is currently undersized. The paucity of assured data and the discontinuous statistical surveys carried out by the National Institute of Statistics (ISTAT) represent one of the main obstacles to the insurance market development. The paper sets forth a parametric model to estimate technical basis for health insurance policies when data are limited and only aggregated information on mortality and morbidity is available. The probabilistic framework is based on a multiple state continuous and time inhomogeneous Markov model. We provide an estimate of transition intensities from the healthy state to the sickness state when only prevalence rates of sickness are available, according to an extension and modification of the methodology proposed in Olivieri (1996) for Long Term Care insurance. We assume that mortality intensity of both healthy and sick lives is modelled by two independent Gompertz–Makeham models.

Suggested Citation

  • Baione, Fabio & Levantesi, Susanna, 2014. "A health insurance pricing model based on prevalence rates: Application to critical illness insurance," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 174-184.
    • Handle: RePEc:eee:insuma:v:58:y:2014:i:c:p:174-184
    DOI: 10.1016/j.insmatheco.2014.07.005
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    References listed on IDEAS

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    1. Helms, Florian & Czado, Claudia & Gschlößl, Susanne, 2005. "Calculation of LTC Premiums Based on Direct Estimates of Transition Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 35(2), pages 455-469, November.
    2. Czado, Claudia & Rudolph, Florian, 2002. "Application of survival analysis methods to long-term care insurance," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 395-413, December.
    3. Pitacco, Ermanno, 1995. "Actuarial models for pricing disability benefits: Towards a unifying approach," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 39-62, April.
    4. Cordeiro, Isabel Maria Ferraz, 2002. "Transition Intensities for a model for Permanent Health Insurance1," ASTIN Bulletin, Cambridge University Press, vol. 32(2), pages 319-346, November.
    5. Marcus Christiansen, 2012. "Multistate models in health insurance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 155-186, June.
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    Cited by:

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    2. Chen, Chang-Chih & Chang, Chia-Chien & Sun, Edward W. & Yu, Min-Teh, 2022. "Optimal decision of dynamic wealth allocation with life insurance for mitigating health risk under market incompleteness," European Journal of Operational Research, Elsevier, vol. 300(2), pages 727-742.
    3. Hsieh, Ming-hua & Wang, Jennifer L. & Chiu, Yu-Fen & Chen, Yen-Chih, 2018. "Valuation of variable long-term care Annuities with Guaranteed Lifetime Withdrawal Benefits: A variance reduction approach," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 246-254.
    4. Peng Yang & Zhiping Chen, 2023. "Optimal Private Health Insurance Contract towards the Joint Interests of a Policyholder and an Insurer," Mathematics, MDPI, vol. 11(10), pages 1-28, May.
    5. Benjiang Ma & Qing Tang & Yifang Qin & Muhammad Farhan Bashir, 2021. "Policyholder cluster divergence based differential premium in diabetes insurance," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(7), pages 1793-1807, October.
    6. Guglielmo D’Amico & Shakti Singh & Dharmaraja Selvamuthu, 2023. "Analysis of fair fee in guaranteed lifelong withdrawal and Markovian health benefits," Annals of Finance, Springer, vol. 19(3), pages 383-400, September.
    7. Valeria D’Amato & Emilia Di Lorenzo & Marilena Sibillo, 2018. "Dread Disease and Cause-Specific Mortality: Exploring New Forms of Insured Loans," Risks, MDPI, vol. 6(1), pages 1-21, February.

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    More about this item

    Keywords

    Multiple state models; Transition intensities; Gompertz–Makeham; Prevalence rates; Critical illness insurance;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • I13 - Health, Education, and Welfare - - Health - - - Health Insurance, Public and Private

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