IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v58y2014icp174-184.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668714000912
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2014.07.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Marcus Christiansen, 2012. "Multistate models in health insurance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 155-186, June.
    3. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Luca Anzilli & Silvio Giove, 2020. "Multi-criteria and medical diagnosis for application to health insurance systems: a general approach through non-additive measures," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 559-582, December.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fuino, Michel & Wagner, Joël, 2018. "Long-term care models and dependence probability tables by acuity level: New empirical evidence from Switzerland," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 51-70.
    2. Guibert, Quentin & Planchet, Frédéric, 2018. "Non-parametric inference of transition probabilities based on Aalen–Johansen integral estimators for acyclic multi-state models: application to LTC insurance," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 21-36.
    3. Maegebier, Alexander, 2013. "Valuation and risk assessment of disability insurance using a discrete time trivariate Markov renewal reward process," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 802-811.
    4. Tomas, Julien & Planchet, Frédéric, 2013. "Multidimensional smoothing by adaptive local kernel-weighted log-likelihood: Application to long-term care insurance," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 573-589.
    5. Boumezoued, Alexandre & Karoui, Nicole El & Loisel, Stéphane, 2017. "Measuring mortality heterogeneity with multi-state models and interval-censored data," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 67-82.
    6. D'Amico, Guglielmo & Singh, Shakti & Selvamuthu, Dharmaraja, 2024. "Optimal investment-disinvestment choices in health-dependent variable annuity," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 1-15.
    7. Manuel L. Esquível & Gracinda R. Guerreiro & Matilde C. Oliveira & Pedro Corte Real, 2021. "Calibration of Transition Intensities for a Multistate Model: Application to Long-Term Care," Risks, MDPI, vol. 9(2), pages 1-17, February.
    8. 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.
    9. Oliver Lunding Sandqvist, 2023. "A multistate approach to disability insurance reserving with information delays," Papers 2312.14324, arXiv.org, revised Jan 2025.
    10. Christiansen, Marcus C. & Djehiche, Boualem, 2020. "Nonlinear reserving and multiple contract modifications in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 187-195.
    11. Ahmad, Jamaal & Bladt, Mogens & Furrer, Christian, 2023. "Aggregate Markov models in life insurance: Properties and valuation," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 50-69.
    12. Frank van Berkum & Katrien Antonio & Michel Vellekoop, 2021. "Quantifying longevity gaps using micro‐level lifetime data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(2), pages 548-570, April.
    13. Martin Eling & Omid Ghavibazoo, 2019. "Research on long-term care insurance: status quo and directions for future research," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 44(2), pages 303-356, April.
    14. Fersini, Paola & Melisi, Giuseppe, 2016. "Stochastic model to evaluate the fair value of motor third-party liability under the direct reimbursement scheme and quantification of the capital requirement in a Solvency II perspective," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 27-44.
    15. Kristian Buchardt & Christian Furrer & Oliver Lunding Sandqvist, 2022. "Transaction time models in multi-state life insurance," Papers 2209.06902, arXiv.org, revised Feb 2023.
    16. Han Hu & Zhao Zhang, 2022. "Long-Term Care Services and Insurance System in China: An Evolutionary Game Analysis," Sustainability, MDPI, vol. 15(1), pages 1-22, December.
    17. Sokol, Alexander, 2015. "A generic model for spouse’s pensions with a view towards the calculation of liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 198-207.
    18. C. Furrer & O. L. Sandqvist, 2025. "Loss of earning capacity in Denmark -- an actuarial perspective," Papers 2501.11578, arXiv.org.
    19. Jang, Jiwook & Mohd Ramli, Siti Norafidah, 2015. "Jump diffusion transition intensities in life insurance and disability annuity," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 440-451.
    20. C Pelletier & T J Chaussalet & H Xie, 2005. "A framework for predicting gross institutional long-term care cost arising from known commitments at local authority level," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(2), pages 144-152, February.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:58:y:2014:i:c:p:174-184. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.