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Modeling stochastic mortality for joint lives through subordinators

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  • Zhang, Yuxin
  • Brockett, Patrick

Abstract

There is a burgeoning literature on mortality models for joint lives. In this paper, we propose a new model in which we use time-changed Brownian motion with dependent subordinators to describe the mortality of joint lives. We then employ this model to estimate the mortality rate of joint lives in a well-known Canadian insurance data set. Specifically, we first depict an individual’s death time as the stopping time when the value of the hazard rate process first reaches or exceeds an exponential random variable, and then introduce the dependence through dependent subordinators. Compared with existing mortality models, this model better interprets the correlation of death between joint lives, and allows more flexibility in the evolution of the hazard rate process. Empirical results show that this model yields highly accurate estimations of mortality compared to the baseline non-parametric (Dabrowska) estimation.

Suggested Citation

  • Zhang, Yuxin & Brockett, Patrick, 2020. "Modeling stochastic mortality for joint lives through subordinators," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 166-172.
    • Handle: RePEc:eee:insuma:v:95:y:2020:i:c:p:166-172
    DOI: 10.1016/j.insmatheco.2020.07.010
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    References listed on IDEAS

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    1. Marilena Sibillo & Emilia Di Lorenzo & Gerarda Tessitore, 2006. "A stochastic proportional hazard model for the force of mortality," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(7), pages 529-536.
    2. T. R. Hurd, 2009. "Credit risk modeling using time-changed Brownian motion," Papers 0904.2376, arXiv.org.
    3. T. R. Hurd, 2009. "Credit Risk Modeling Using Time-Changed Brownian Motion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(08), pages 1213-1230.
    4. Linda L. Golden & Patrick L. Brockett & Jing Ai & Bruce Kellison, 2016. "Empirical Evidence on the Use of Credit Scoring for Predicting Insurance Losses with Psycho-social and Biochemical Explanations," North American Actuarial Journal, Taylor & Francis Journals, vol. 20(3), pages 233-251, July.
    5. Luciano, Elisa & Spreeuw, Jaap & Vigna, Elena, 2008. "Modelling stochastic mortality for dependent lives," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 234-244, October.
    6. Manor, Orly & Eisenbach, Zvi, 2003. "Mortality after spousal loss: are there socio-demographic differences?," Social Science & Medicine, Elsevier, vol. 56(2), pages 405-413, January.
    7. Patrizia Semeraro, 2008. "A Multivariate Variance Gamma Model For Financial Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-18.
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    Cited by:

    1. Ying Jiao & Yahia Salhi & Shihua Wang, 2022. "Dynamic Bivariate Mortality Modelling," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 917-938, June.

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    More about this item

    Keywords

    Mortality rate; Joint lives; Survival; Stochastic process; Subordinator;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • I1 - Health, Education, and Welfare - - Health
    • J1 - Labor and Demographic Economics - - Demographic Economics

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