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Heterogeneity and uncertainty in a multistate framework

Author

Listed:
  • D. Tabakova

    (MIB Trieste School of Management)

  • E. Pitacco

    (University of Trieste)

Abstract

This research develops the scheme proposed in the paper Pollard [J Inst Actuar 96(2): 251–264, 1970], which is based on a two-state model for the analysis of 1-year mortality, but the results are also valid for the probabilities related to other types of insurance events such as disablement and accidents. We extend the Pollard’s original scheme into time-discrete models with more states (active-invalid-dead) together with further investigation into multi-year time horizon. Additionally, hypotheses for real-valued individual frailty are assumed in the models. As the baseline probabilistic structure, we have adopted a traditional three-state model in a Markov context. We focus on an insurance portfolio. Our outputs of interest are based on the probability distributions of the annual payouts for term insurance policies providing lump sum benefits both in case of death and in case of permanent disability. The analysis of the probability distributions allows us to assess the risk profile of the insurance portfolio, and thus to suggest appropriate actions in terms of premiums and capital allocation. In this regards, we adopt the percentile principle.

Suggested Citation

  • D. Tabakova & E. Pitacco, 2021. "Heterogeneity and uncertainty in a multistate framework," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 117-139, June.
    • Handle: RePEc:spr:decfin:v:44:y:2021:i:1:d:10.1007_s10203-020-00306-7
    DOI: 10.1007/s10203-020-00306-7
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    References listed on IDEAS

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    1. Denuit, Michel & Lucas, Nathalie & Pitacco, Ermanno, 2019. "Pricing and Reserving in LTC Insurance," LIDAM Reprints ISBA 2019030, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Amitabh Chandra & Andrew A. Samwick, 2009. "Disability Risk and the Value of Disability Insurance," NBER Chapters, in: Health at Older Ages: The Causes and Consequences of Declining Disability among the Elderly, pages 295-336, National Bureau of Economic Research, Inc.
    3. Olivieri, Annamaria & Pitacco, Ermanno, 2009. "Stochastic Mortality: The Impact on Target Capital," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 541-563, November.
    4. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
    5. Pitacco, Ermanno & Denuit, Michel & Haberman, Steven & Olivieri, Annamaria, 2009. "Modelling Longevity Dynamics for Pensions and Annuity Business," OUP Catalogue, Oxford University Press, number 9780199547272.
    Full references (including those not matched with items on IDEAS)

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