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Mortality Surface by Means of Continuous Time Cohort Models

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  • Petar Jevtic
  • Elisa Luciano
  • Elena Vigna

Abstract

We study and calibrate a cohort-based model which captures the characteristics of a mortality surface with a parsimonious, continuous-time fac- tor approach. The model allows for imperfect correlation of mortality intensity across generations. It is implemented on UK data for the period 1900-2008. Calibration by means of stochastic search and the Differential Evolution opti- mization algorithm proves to yield robust and stable parameters. We provide in-sample and out-of-sample, deterministic as well as stochastic forecasts. Cal- ibration confirms that correlation across generations is smaller than one.

Suggested Citation

  • Petar Jevtic & Elisa Luciano & Elena Vigna, 2012. "Mortality Surface by Means of Continuous Time Cohort Models," Carlo Alberto Notebooks 264, Collegio Carlo Alberto, revised 2013.
    • Handle: RePEc:cca:wpaper:264
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    References listed on IDEAS

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    Cited by:

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    2. Man Chung Fung & Katja Ignatieva & Michael Sherris, 2015. "Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives," Papers 1508.00090, arXiv.org.
    3. Cupido, Kyran & Jevtić, Petar & Paez, Antonio, 2020. "Spatial patterns of mortality in the United States: A spatial filtering approach," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 28-38.
    4. Yajing Xu & Michael Sherris & Jonathan Ziveyi, 2020. "Market Price of Longevity Risk for a Multi‐Cohort Mortality Model With Application to Longevity Bond Option Pricing," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 87(3), pages 571-595, September.
    5. Jevtić, Petar & Regis, Luca, 2019. "A continuous-time stochastic model for the mortality surface of multiple populations," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 181-195.
    6. Petar Jevtić & Luca Regis, 2021. "A Square-Root Factor-Based Multi-Population Extension of the Mortality Laws," Mathematics, MDPI, vol. 9(19), pages 1-17, September.
    7. Anastasia Novokreshchenova, 2016. "Predicting Human Mortality: Quantitative Evaluation of Four Stochastic Models," Risks, MDPI, vol. 4(4), pages 1-28, December.
    8. Yang Chang & Michael Sherris, 2018. "Longevity Risk Management and the Development of a Value-Based Longevity Index," Risks, MDPI, vol. 6(1), pages 1-20, February.
    9. Daniel H. Alai & Katja Ignatieva & Michael Sherris, 2019. "The Investigation of a Forward-Rate Mortality Framework," Risks, MDPI, vol. 7(2), pages 1-22, June.
    10. Wang, Ling & Chiu, Mei Choi & Wong, Hoi Ying, 2021. "Volterra mortality model: Actuarial valuation and risk management with long-range dependence," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 1-14.
    11. Hainaut, Donatien, 2022. "A calendar year mortality model in continuous time," LIDAM Discussion Papers ISBA 2022019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. De Rosa, Clemente & Luciano, Elisa & Regis, Luca, 2021. "Geographical Diversification And Longevity Risk Mitigation In Annuity Portfolios," ASTIN Bulletin, Cambridge University Press, vol. 51(2), pages 375-410, May.
    13. Milevsky, Moshe A., 2020. "Calibrating Gompertz in reverse: What is your longevity-risk-adjusted global age?," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 147-161.
    14. Paul Doukhan & Joseph Rynkiewicz & Yahia Salhi, 2021. "Optimal Neighborhood Selection for AR-ARCH Random Fields with Application to Mortality," Stats, MDPI, vol. 5(1), pages 1-26, December.
    15. Helena Chuliá & Montserrat Guillén & Jorge M. Uribe, 2015. "Mortality and Longevity Risks in the United Kingdom: Dynamic Factor Models and Copula-Functions," Working Papers 2015-03, Universitat de Barcelona, UB Riskcenter.
    16. Doukhan, P. & Pommeret, D. & Rynkiewicz, J. & Salhi, Y., 2017. "A class of random field memory models for mortality forecasting," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 97-110.
    17. Fadoua Zeddouk & Pierre Devolder, 2020. "Longevity Modelling and Pricing under a Dependent Multi-Cohort Framework," Risks, MDPI, vol. 8(4), pages 1-23, November.
    18. Ling Wang & Mei Choi Chiu & Hoi Ying Wong, 2020. "Volterra mortality model: Actuarial valuation and risk management with long-range dependence," Papers 2009.09572, arXiv.org.
    19. Zhiping Huang & Michael Sherris & Andrés M. Villegas & Jonathan Ziveyi, 2022. "Modelling USA Age-Cohort Mortality: A Comparison of Multi-Factor Affine Mortality Models," Risks, MDPI, vol. 10(9), pages 1-28, September.
    20. Elisa Luciano & Luca Regis, 2012. "Demographic risk transfer: is it worth for annuity providers?," ICER Working Papers 11-2012, ICER - International Centre for Economic Research.
    21. Luca Regis, 2014. "Demographic uncertainty, the financing mix and the sustainability of welfare systems," Working Papers SWITCH 02-2014, Competitività, Regole, Mercati (CERM).

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    More about this item

    Keywords

    stochastic mortality; age effect; cohort effect; differential evolution algorithm; mortality forecasting.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts

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