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Modeling Disability in Long-Term Care Insurance

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  • D. J. Pritchard

Abstract

Long-term care (LTC) costs and, in particular, those arising under an LTC insurance contract, are difficult to estimate. This is because of the complex effects of the processes of aging—disability and cognitive impairment. As disability is a gradual, as opposed to a discrete, process, and as the effects are sometimes reversible, a fairly complex model is necessary to capture its nature. This paper concentrates on modeling the disability process of aging only and, in particular, fully incorporates the recovery process as dictated by the data. With the recovery process modeled, the effect on the estimated model costs of disability of the common simplifying assumption that recoveries can be ignored is easily assessed.This paper has twin objectives: (1) to present novel methodology, the penalized likelihood, for using interval-censored longitudinal data, such as the National Long-Term Care Study, to parameterize Markov models; and (2) to estimate the costs arising under an LTC insurance contract in respect of disability. The model is also used to show that ignoring recovery from disability can lead to significant overestimation of LTC insurance costs—suggesting that claims underwriting in LTC insurance may be an important factor in managing claims costs.

Suggested Citation

  • D. J. Pritchard, 2006. "Modeling Disability in Long-Term Care Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(4), pages 48-75.
  • Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:48-75
    DOI: 10.1080/10920277.2006.10597413
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. William Lim & Gaurav Khemka & David Pitt & Bridget Browne, 2019. "A method for calculating the implied no-recovery three-state transition matrix using observable population mortality incidence and disability prevalence rates among the elderly," Journal of Population Research, Springer, vol. 36(3), pages 245-282, September.
    4. Jason Brown & Mark Warshawsky, 2013. "The Life Care Annuity: A New Empirical Examination of an Insurance Innovation That Addresses Problems in the Markets for Life Annuities and Long-Term Care Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 677-704, September.
    5. 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.
    6. 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.
    7. Ermanno Pitacco, 2016. "Premiums for Long-Term Care Insurance Packages: Sensitivity with Respect to Biometric Assumptions," Risks, MDPI, vol. 4(1), pages 1-22, February.
    8. Shao, Adam W. & Chen, Hua & Sherris, Michael, 2019. "To borrow or insure? Long term care costs and the impact of housing," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 15-34.
    9. Manuel L. Esquível & Nadezhda P. Krasii & Gracinda R. Guerreiro, 2021. "Open Markov Type Population Models: From Discrete to Continuous Time," Mathematics, MDPI, vol. 9(13), pages 1-29, June.
    10. 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.

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