IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v9y2021i2p37-d495746.html
   My bibliography  Save this article

Calibration of Transition Intensities for a Multistate Model: Application to Long-Term Care

Author

Listed:
  • Manuel L. Esquível

    (FCT NOVA, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal
    CMA-FCT-UNL, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal
    These authors contributed equally to this work.)

  • Gracinda R. Guerreiro

    (FCT NOVA, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal
    CMA-FCT-UNL, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal
    These authors contributed equally to this work.)

  • Matilde C. Oliveira

    (FCT NOVA, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal
    These authors contributed equally to this work.)

  • Pedro Corte Real

    (FCT NOVA, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal
    These authors contributed equally to this work.)

Abstract

We consider a non-homogeneous continuous time Markov chain model for Long-Term Care with five states: the autonomous state, three dependent states of light , moderate and severe dependence levels and the death state. For a general approach, we allow for non null intensities for all the returns from higher dependence levels to all lesser dependencies in the multi-state model. Using data from the 2015 Portuguese National Network of Continuous Care database, as the main research contribution of this paper, we propose a method to calibrate transition intensities with the one step transition probabilities estimated from data. This allows us to use non-homogeneous continuous time Markov chains for modeling Long-Term Care. We solve numerically the Kolmogorov forward differential equations in order to obtain continuous time transition probabilities. We assess the quality of the calibration using the Portuguese life expectancies. Based on reasonable monthly costs for each dependence state we compute, by Monte Carlo simulation, trajectories of the Markov chain process and derive relevant information for model validation and premium calculation.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:2:p:37-:d:495746
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/9/2/37/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/9/2/37/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Denis Kessler, 2008. "The Long-Term Care Insurance Market," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 33(1), pages 33-40, January.
    2. 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.
    3. Dickson,David C. M. & Hardy,Mary R. & Waters,Howard R., 2013. "Solutions Manual for Actuarial Mathematics for Life Contingent Risks," Cambridge Books, Cambridge University Press, number 9781107620261, February.
    4. Montserrat Guillén & Jean Pinquet, 2008. "Long-Term Care: Risk Description of a Spanish Portfolio and Economic Analysis of the Timing of Insurance Purchase," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 33(4), pages 659-672, October.
    5. Andy Zuchandke & Sebastian Reddemann & Simone Krummaker, 2012. "Financing Long-Term Care in Germany," Palgrave Macmillan Books, in: Joan Costa-Font & Christophe Courbage (ed.), Financing Long-Term Care in Europe, chapter 12, pages 214-235, Palgrave Macmillan.
    6. Joelle H. Fong & Adam W. Shao & Michael Sherris, 2015. "Multistate Actuarial Models of Functional Disability," North American Actuarial Journal, Taylor & Francis Journals, vol. 19(1), pages 41-59, January.
    7. Bravo, Jorge M. & Ayuso, Mercedes & Holzmann, Robert & Palmer, Edward, 2021. "Addressing the life expectancy gap in pension policy," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 200-221.
    8. Ardo van den Hout & Ekaterina Ogurtsova & Jutta Gampe & Fiona Matthews, 2014. "Investigating healthy life expectancy using a multi-state model in the presence of missing data and misclassification," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(42), pages 1219-1244.
    9. Henri de Castries, 2009. "Ageing and Long-Term Care: Key Challenges in Long-Term Care Coverage for Public and Private Systems," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 34(1), pages 24-34, January.
    10. Dickson,David C. M. & Hardy,Mary R. & Waters,Howard R., 2013. "Actuarial Mathematics for Life Contingent Risks," Cambridge Books, Cambridge University Press, number 9781107044074, October.
    11. H. Xie & T. J. Chaussalet & P. H. Millard, 2005. "A continuous time Markov model for the length of stay of elderly people in institutional long‐term care," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(1), pages 51-61, January.
    12. Olivia S Mitchell & John Piggott & Satoshi Shimizutani, 2008. "An Empirical Analysis of Patterns in the Japanese Long-Term Care Insurance System," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 33(4), pages 694-709, October.
    13. Marcus Christiansen, 2012. "Multistate models in health insurance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 155-186, June.
    14. Joan Costa-Font & Christophe Courbage (ed.), 2012. "Financing Long-Term Care in Europe," Palgrave Macmillan Books, Palgrave Macmillan, number 978-0-230-34919-3, October.
    15. 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.
    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. G. Apicella & A. Molent & M. Gaudenzi, 2024. "The Life Care Annuity: enhancing product features and refining pricing methods," Papers 2404.02858, arXiv.org, revised May 2024.
    2. Ventura-Marco, Manuel & Vidal-Meliá, Carlos & Pérez-Salamero González, Juan Manuel, 2023. "Joint life care annuities to help retired couples to finance the cost of long-term care," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 122-139.
    3. 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.

    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. 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.
    3. 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.
    4. Qiqi Wang & Katja Hanewald & Xiaojun Wang, 2022. "Multistate health transition modeling using neural networks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(2), pages 475-504, June.
    5. Jin Sun & Eckhard Platen, 2019. "Benchmarked Risk Minimizing Hedging Strategies for Life Insurance Policies," Research Paper Series 399, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Justina Klimaviciute & Pierre Pestieau & Jérôme Schoenmaeckers, 2019. "Family altruism and long-term care insurance," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 44(2), pages 216-230, April.
    7. 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.
    8. Christophe Courbage & Guillem Montoliu-Montes & Joël Wagner, 2020. "The effect of long-term care public benefits and insurance on informal care from outside the household: empirical evidence from Italy and Spain," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 21(8), pages 1131-1147, November.
    9. Raj Kumari Bahl & Sotirios Sabanis, 2017. "General Price Bounds for Guaranteed Annuity Options," Papers 1707.00807, arXiv.org.
    10. Lee, Hangsuck & Ahn, Jae Youn & Ko, Bangwon, 2019. "Construction of multiple decrement tables under generalized fractional age assumptions," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 104-119.
    11. Jean Pinquet, 2008. "Quel avenir pour l'assurance dépendance? Leçons de l'expérience américaine," Post-Print hal-00396151, HAL.
    12. Deelstra, Griselda & Grasselli, Martino & Van Weverberg, Christopher, 2016. "The role of the dependence between mortality and interest rates when pricing Guaranteed Annuity Options," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 205-219.
    13. Thomas Bernhardt & Catherine Donnelly, 2019. "Modern tontine with bequest: innovation in pooled annuity products," Papers 1903.05990, arXiv.org.
    14. Chandoevwit, Worawan & Wasi, Nada, 2020. "Incorporating discrete choice experiments into policy decisions: Case of designing public long-term care insurance," Social Science & Medicine, Elsevier, vol. 258(C).
    15. Barigou, Karim & Goffard, Pierre-Olivier & Loisel, Stéphane & Salhi, Yahia, 2023. "Bayesian model averaging for mortality forecasting using leave-future-out validation," International Journal of Forecasting, Elsevier, vol. 39(2), pages 674-690.
    16. Fuino, Michel & Wagner, Joël, 2020. "Duration of long-term care: Socio-economic factors, type of care interactions and evolution," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 151-168.
    17. Carole Bernard & Adam Kolkiewicz & Junsen Tang, 2023. "Valuation of Reverse Mortgages with Default Risk Models," The Journal of Real Estate Finance and Economics, Springer, vol. 66(4), pages 806-839, May.
    18. Wang, Suxin & Lu, Yi & Sanders, Barbara, 2018. "Optimal investment strategies and intergenerational risk sharing for target benefit pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 1-14.
    19. He, Lin & Liang, Zongxia & Wang, Sheng, 2022. "Dynamic optimal adjustment policies of hybrid pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 46-68.

    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:gam:jrisks:v:9:y:2021:i:2:p:37-:d:495746. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.