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Frailty and Risk Classification for Life Annuity Portfolios


  • Annamaria Olivieri

    () (Department of Economics, University of Parma, Via J.F. Kennedy 6, 43125 Parma, Italy)

  • Ermanno Pitacco

    () (DEAMS ‘B. de Finetti’, University of Trieste, Via dell’Università 1, 34100 Trieste, Italy)


Life annuities are attractive mainly for healthy people. In order to expand their business, in recent years, some insurers have started offering higher annuity rates to those whose health conditions are critical. Life annuity portfolios are then supposed to become larger and more heterogeneous. With respect to the insurer’s risk profile, there is a trade-off between portfolio size and heterogeneity that we intend to investigate. In performing this, there is a second and possibly more important issue that we address. In actuarial practice, the different mortality levels of the several risk classes are obtained by applying adjustment coefficients to population mortality rates. Such a choice is not supported by a rigorous model. On the other hand, the heterogeneity of a population with respect to mortality can formally be described with a frailty model. We suggest adopting a frailty model for risk classification. We identify risk groups (or classes) within the population by assigning specific ranges of values to the frailty within each group. The different levels of mortality of the various groups are based on the conditional probability distributions of the frailty. Annuity rates for each class then can be easily justified, and a comprehensive investigation of insurer’s liabilities can be performed.

Suggested Citation

  • Annamaria Olivieri & Ermanno Pitacco, 2016. "Frailty and Risk Classification for Life Annuity Portfolios," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-23, October.
  • Handle: RePEc:gam:jrisks:v:4:y:2016:i:4:p:39-:d:81388

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    References listed on IDEAS

    1. A. R. Thatcher, 1999. "The long-term pattern of adult mortality and the highest attained age," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(1), pages 5-43.
    2. Meyricke, Ramona & Sherris, Michael, 2013. "The determinants of mortality heterogeneity and implications for pricing annuities," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 379-387.
    3. David Steinsaltz & Kenneth Wachter, 2006. "Understanding Mortality Rate Deceleration and Heterogeneity," Mathematical Population Studies, Taylor & Francis Journals, vol. 13(1), pages 19-37.
    4. Butt, Zoltan & Haberman, Steven, 2004. "Application of Frailty-Based Mortality Models Using Generalized Linear Models," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 34(01), pages 175-197, May.
    5. 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.
    6. Pitacco, Ermanno & Denuit, Michel & Haberman, Steven & Olivieri, Annamaria, 2009. "Modelling Longevity Dynamics for Pensions and Annuity Business," OUP Catalogue, Oxford University Press, number 9780199547272.
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    More about this item


    voluntary annuities; underwritten annuities; heterogeneity; standard risk; substandard risk; preferred risk; issue-select mortality rates;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • G0 - Financial Economics - - General
    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G3 - Financial Economics - - Corporate Finance and Governance
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics
    • M4 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting
    • K2 - Law and Economics - - Regulation and Business Law


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