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Sur une classe de transformations itérées pour l'ajustement et la simulation stochastique

Author

Listed:
  • Alexis Bienvenüe

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Didier Rullière

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

Nous proposons une classe paramétrée de distorsions de probabilités qui permettent, itérées, de s'approcher aussi finement que voulu d'une fonction de survie cible. Par construction, la classe proposée respecte plusieurs propriétés que nous détaillons, et en particulier l'inversibilité analytique et la stabilité dont nous présentons l'intérêt pour certaines études actuarielles. Nous étudions l'impact asymptotique de ces distorsions sur le taux de hasard. Nous formulons les conditions sous lesquelles distorsions proposées constituent la base d'un indicateur de risque. Nous établissons la forme des compositions de distorsions ainsi que la convergence de la loi initiale déformée vers la loi cible. Une méthodologie d'estimation et des valeurs d'initialisations sont proposées. Des applications à l'analyse de la mortalité fournissent des résultats pour la modélisation d'évènements catastrophiques, ainsi que des représentations paramétrées très fidèles de l'évolution des lois de mortalité au fil des ans. Une analyse de l'impact de la paramétrisation choisie est également conduite. Nous suggérons finalement un modèle de simulation de mortalité prospective qui découle des constructions précédentes.

Suggested Citation

  • Alexis Bienvenüe & Didier Rullière, 2009. "Sur une classe de transformations itérées pour l'ajustement et la simulation stochastique," Working Papers hal-00395495, HAL.
    • Handle: RePEc:hal:wpaper:hal-00395495
    Note: View the original document on HAL open archive server: https://hal.science/hal-00395495
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    References listed on IDEAS

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    1. Jong, Piet De & Marshall, Claymore, 2007. "Mortality Projection Based on the Wang Transform," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 149-161, May.
    2. Goovaerts, Marc J. & Kaas, Rob & Dhaene, Jan & Tang, Qihe, 2004. "Some new classes of consistent risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 505-516, June.
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