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Copula models of joint last survivor analysis

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  • Arkady E. Shemyakin
  • Heekyung Youn

Abstract

Copula models are becoming increasingly popular for modelling dependencies between random variables. The range of their recent applications includes such fields as analysis of extremes in financial assets and returns; failure of paired organs in health science; reliability studies; and human mortality in insurance. This paper gives a brief overview of the principles of construction of such copula models as Gaussian, Student, and Archimedean. The latter includes Frank, Clayton, and stable (Gumbel–Hougaard) families. The emphasis is on application of copula models to joint last survivor analysis. The main example discussed in this paper deals with the mortality of spouses, known to be associated through such factors as common disaster, common lifestyle, or the broken‐heart syndrome. These factors suggest modelling dependence of spouses' lives on both calendar date scale and age‐at‐death scale. This dependence structure suggests a different treatment than that for problems of survival analysis such as paired organ failure or twins' mortality. Construction of a conditional Bayesian copula model is further generalized in view of the relationship between the joint first life and last surviror probabilities. A numerical example is considered, involving the implementation of Markov chain Monte Carlo algorithms using WinBUGs. Copyright © 2006 John Wiley & Sons, Ltd.

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  • Arkady E. Shemyakin & Heekyung Youn, 2006. "Copula models of joint last survivor analysis," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 22(2), pages 211-224, March.
    • Handle: RePEc:wly:apsmbi:v:22:y:2006:i:2:p:211-224
    DOI: 10.1002/asmb.629
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    Cited by:

    1. Chen, Hua & MacMinn, Richard & Sun, Tao, 2015. "Multi-population mortality models: A factor copula approach," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 135-146.
    2. Gourieroux, Christian & Lu, Yang, 2015. "Love and death: A Freund model with frailty," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 191-203.
    3. Chen, Li & Lin, Luyao & Lu, Yi & Parker, Gary, 2017. "Analysis of survivorship life insurance portfolios with stochastic rates of return," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 16-31.
    4. Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2012. "Evolution of coupled lives' dependency across generations and pricing impact," Carlo Alberto Notebooks 258, Collegio Carlo Alberto.
    5. Ying Jiao & Yahia Salhi & Shihua Wang, 2021. "Dynamic Bivariate Mortality Modelling," Working Papers hal-03244324, HAL.
    6. Gobbi, Fabio & Kolev, Nikolai & Mulinacci, Sabrina, 2021. "Ryu-type extended Marshall-Olkin model with implicit shocks and joint life insurance applications," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 342-358.
    7. 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.
    8. Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2016. "Spouses’ Dependence across Generations and Pricing Impact on Reversionary Annuities," Risks, MDPI, vol. 4(2), pages 1-18, May.

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