Iterative Adjustment of Survival Functions by Composed Probability Distortions

Alexis Bienvenüe (1) , Didier Rullière (1)

1 SAF - Laboratoire de Sciences Actuarielle et Financière

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.

Mots clés: probability distortions; mortality; iterated compositions; hyperbolic transform; risk measure; survival function transformation

Domaines: Economies et finances; Gestion des risques [q-fin.RM]

Alexis Bienvenüe, Didier Rullière. Iterative Adjustment of Survival Functions by Composed Probability Distortions. The Geneva Risk and Insurance Review, 2012, 37 (2), pp.156-179. ⟨10.1057/grir.2011.7⟩. ⟨hal-00665890⟩