Skip to main content

Advertisement

SpringerLink
Log in

A Stochastic Model for Mortality Rate on Italian Data

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Milevesky, M.A., Promislow, S.D.: Mortality derivatives and the option to annuitise. Insur. Math. Econ. 29, 299–318 (2001)

    Article  Google Scholar 

  2. Wymer, C.R.: Econometric estimation of stochastic differential equation systems. Econometrica 40(3), 565–577 (1972)

    Article  MATH  Google Scholar 

  3. JPMorgan: LifeMetrics. A toolkit for measuring and managing longevity and mortality risks, V1.0 (2007)

  4. Lee, R.D., Carter, L.R.: Modelling and forecasting U.S. mortality. J. Am. Stat. Assoc. 87, 659–671 (1992)

    Article  Google Scholar 

  5. Lee, R.D.: The Lee-Carter method for forecasting mortality, with various extensions and applications. N. Am. Actuar. J. 4, 80–93 (2000)

    MathSciNet  MATH  Google Scholar 

  6. Renshaw, A.E., Habermann, S.: A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insur. Math. Econ. 38, 556–570 (2006)

    Article  MATH  Google Scholar 

  7. Cairns, A.J.G.: A discussion of parameters and model uncertainty. Insur. Math. Econ. 27, 313–330 (2000)

    Article  MATH  Google Scholar 

  8. Cairns, A.J.G., Blake, D., Dowd, K.: A two factor model for stochastic mortality with parameter uncertainty: theory and calibration. J. Risk Insur. 73, 687–718 (2006)

    Article  Google Scholar 

  9. Currie, I.G.: Smoothing and forecasting mortality rates with P-splines. Available on line at www.ma.hw.ac.uk/iain/research/talks.html (2006)

  10. Plat, R.: Stochastic portfolio specific mortality and the quantification of mortality basis risk. Available on line at http://ssrn.com/abstract=1277803 (2009)

  11. Cairns, A.J.G., Blake, D., Dowd, K.: Pricing death: frameworks for the valuation and securitization of mortality risk, Centre for Risk & Insurance Studies. CRIS Discussion Paper Series, No. IV, The University of Nottingham (2006)

  12. Biffis, E.: Affine processes for dynamic mortality and actuarial valuations. Insur. Math. Econ. 37, 443–468 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ballotta, L., Habermann, S.: The fair valuation problem of guaranteed annuity options: the stochastic mortality environment case. Insur. Math. Econ. 38, 195–214 (2006)

    Article  MATH  Google Scholar 

  14. Luciano, E., Vigna, E.: Non mean reverting affine processes for stochastic mortality. Belg. Actuar. Bull. 8(1), 5–16 (2008)

    Google Scholar 

  15. Gompertz, B.: On the nature of function expressive of the law of human mortality and on a new mode of determining the value of life contingencies. Philos. Trans. R. Soc. Lond. 123, 513–585 (1832)

    Google Scholar 

  16. Sargan, J.D.: Some discrete approximations to continuous time stochastic models. J. R. Stat. Soc. B 36, 74–90 (1975)

    MathSciNet  Google Scholar 

  17. Seber, G.A.F., Wild, C.J.: Non linear regression. Wiley, New York (1989)

    Google Scholar 

  18. Biggs, M.C.: Constrained minimization using recursive quadratic programming. In: Dixon, L.C.W., Szegö, G.P. (eds.) Towards Global Optimization, pp. 341–349. North Holland, Amsterdam (1975)

    Google Scholar 

  19. Powell, M.J.D.: The convergence of variable metric methods for nonlinearly constrained optimization calculations. In: Mangasarian, O.L., Meyer, R.R., Robinson, S.M. (eds.) Non Linear Programming 3, pp. 27–63. Academic Press, New York (1978)

    Google Scholar 

  20. Powell, M.J.D.: A fast algorithm for nonlinearly constrained optimization calculations. In: Watson, G.A. (ed.) Numerical Analysis. Lecture Notes in Mathematics, vol. 630, pp. 144–157. Springer, Berlin (1978)

    Chapter  Google Scholar 

  21. Ortobelli, S.: The classification of parametric choices under uncertainty: analysis of the portfolio choice problem. Theory Decis. 51, 297–327 (2001)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Statistics, Computer Science, and Applications, University of Bergamo, Via dei Caniana 2, Bergamo, 24127, Italy

    R. Giacometti, S. Ortobelli & M. Bertocchi

Authors
  1. R. Giacometti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Ortobelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Bertocchi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Bertocchi.

Additional information

Communicated by F. Zirilli.

The authors greatly acknowledge the national grant from the Ministry of Education and Research: Financial innovations and demographic changes: new products and pricing instruments with respect to the stochastic factor aging (local coordinator M. Bertocchi) as well as grants from University of Bergamo 2008, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Giacometti, R., Ortobelli, S. & Bertocchi, M. A Stochastic Model for Mortality Rate on Italian Data. J Optim Theory Appl 149, 216–228 (2011). https://doi.org/10.1007/s10957-010-9771-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-010-9771-5

Keywords

Search

Navigation