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Iterative Adjustment of Survival Functions by Composed Probability Distortions

Author

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  • Alexis Bienvenüe

    (Laboratoire SAF, Institut de Science Financière et d’Assurances, Université de Lyon, Université Lyon 1, EA 2429, 50 Avenue Tony Garnier, Lyon F-69007, France. E-mails: Alexis.Bienvenue@univ-lyon1.fr; Didier.Rulliere@univ-lyon1.fr)

  • Didier Rullière

    (Laboratoire SAF, Institut de Science Financière et d’Assurances, Université de Lyon, Université Lyon 1, EA 2429, 50 Avenue Tony Garnier, Lyon F-69007, France. E-mails: Alexis.Bienvenue@univ-lyon1.fr; Didier.Rulliere@univ-lyon1.fr)

Abstract

We introduce a parametric class of composite probability distortions that can be combined to converge to a target survival function. These distortions respect analytic invertibility and stability, which are shown to be relevant in many actuarial fields. We study the asymptotic impact of such distortions on hazard rates. The paper provides an estimation methodology, including hints for initialisation. Some applications to survival data bring results for catastrophic event impact modelling. We also obtain accurate parametric representations of the mortality trend over years. Finally, we suggest a prospective mortality simulation model that comes naturally from the above analysis.

Suggested Citation

  • Alexis Bienvenüe & Didier Rullière, 2012. "Iterative Adjustment of Survival Functions by Composed Probability Distortions," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 37(2), pages 156-179, September.
    • Handle: RePEc:pal:genrir:v:37:y:2012:i:2:p:156-179
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    Cited by:

    1. repec:hal:wpaper:hal-00834000 is not listed on IDEAS
    2. Di Bernardino Elena & Rullière Didier, 2013. "On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators," Dependence Modeling, De Gruyter, vol. 1(2013), pages 1-36, October.
    3. Elena Di Bernardino & Didier Rullière, 2012. "Distortions of multivariate risk measures: a level-sets based approach," Working Papers hal-00756387, HAL.
    4. Di Bernardino, Elena & Rullière, Didier, 2013. "Distortions of multivariate distribution functions and associated level curves: Applications in multivariate risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 190-205.
    5. repec:hal:wpaper:hal-00750873 is not listed on IDEAS

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