On hyperbolic iterated distortions for the adjustment of survival functions

Alexis Bienvenüe () and Didier Rullière ()
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Alexis Bienvenüe: University of Lyon, University of Lyon 1, Ecole ISFA, Lab. SAF, EA2429
Didier Rullière: University of Lyon, University of Lyon 1, Ecole ISFA, Lab. SAF, EA2429

A chapter in Mathematical and Statistical Methods for Actuarial Sciences and Finance, 2012, pp 35-42 from Springer

Abstract: Abstract This paper presents a class of distortions of survival functions. Studied distortions are built in order to respect several properties that seem to us useful in actuarial science. We focus here on some particular hyperbolic distortions, which preserve analytic invertibility of the distorted survival function, and for which inverse distortions belong to the same hyperbolic class. We propose some specific parameterizations of these distortions which give a straightforward inversion, and discuss the importance of such an inversion in insurance and finance. We prove the convergence of composed distortions to any target law, and give initial values and a particular methodology for the parameters estimation. Numerical figures illustrate the adaptation of these distortions to several actuarial fields.

Keywords: Probability distortions; iterated compositions; hyperbolic transform; risk measure; survival function transformation; conversion function (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-88-470-2342-0_5

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DOI: 10.1007/978-88-470-2342-0_5

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