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

Author

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  • 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
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    References listed on IDEAS

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    1. G. Apicella & A. Molent & M. Gaudenzi, 2024. "The Life Care Annuity: enhancing product features and refining pricing methods," Papers 2404.02858, arXiv.org.
    2. 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.

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