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A Stochastic Model for Mortality Rate on Italian Data

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  • R. Giacometti

    (University of Bergamo)

  • S. Ortobelli

    (University of Bergamo)

  • M. Bertocchi

    (University of Bergamo)

Abstract

A new stochastic model for mortality rate is proposed and analyzed on Italian mortality data. The model is based on a stochastic differential equation derived from a generalization of the Milevesky and Promislow model (Milevesky, M.A., Promislow, S.D.: Insur. Math. Econ. 29, 299–318 (2001)). We discuss and present a methodology, based on the discretisation approach by Wymer (Wymer, C.R.: Econometrica 40(3), 565–577 (1972)) to evaluate the parameters of our model. The comparison with the Milevesky and Promislow model shows the relevance of our proposal along an horizon, which includes periods of time with a different volatility of mortality rates. The estimate of the parameters turns out to be stable over time with the exception of the mean reverting parameter, which shows, for a person of a fixed age, an increase over time.

Suggested Citation

  • R. Giacometti & S. Ortobelli & M. Bertocchi, 2011. "A Stochastic Model for Mortality Rate on Italian Data," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 216-228, April.
    • Handle: RePEc:spr:joptap:v:149:y:2011:i:1:d:10.1007_s10957-010-9771-5
    DOI: 10.1007/s10957-010-9771-5
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    References listed on IDEAS

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    1. Wymer, C R, 1972. "Econometric Estimation of Stochastic Differential Equation Systems," Econometrica, Econometric Society, vol. 40(3), pages 565-577, May.
    2. Plat, Richard, 2009. "Stochastic portfolio specific mortality and the quantification of mortality basis risk," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 123-132, August.
    3. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 79-120, May.
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    7. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two‐Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718, December.
    8. Ballotta, Laura & Haberman, Steven, 2006. "The fair valuation problem of guaranteed annuity options: The stochastic mortality environment case," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 195-214, February.
    9. Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 299-318, December.
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    Cited by:

    1. Russo, Vincenzo & Giacometti, Rosella & Ortobelli, Sergio & Rachev, Svetlozar & Fabozzi, Frank J., 2011. "Calibrating affine stochastic mortality models using term assurance premiums," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 53-60, July.

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