Estimating the distortion parameter of the proportional-hazard premium for heavy-tailed losses

Brahim Brahimi, Djamel Meraghni, Abdelhakim Necir and Ričardas Zitikis

Insurance: Mathematics and Economics, 2011, vol. 49, issue 3, 325-334

Abstract: The distortion parameter reflects the amount of loading in insurance premiums. A specific value of a given premium determines a value of the distortion parameter, which depends on the underlying loss distribution. Estimating the parameter, therefore, becomes a statistical inferential problem, which has been initiated by Jones and Zitikis [Jones, B.L., Zitikis, R., 2007. Risk measures, distortion parameters, and their empirical estimation. Insurance: Mathematics and Economics, 41, 279–297] in the case of the distortion premium and tackled within the framework of the central limit theorem. Heavy-tailed losses do not fall into this framework as they rely on the extreme-value theory. In this paper, we concentrate on a special but important distortion premium, called the proportional-hazard premium, and propose an estimator for its distortion parameter in the case of heavy-tailed losses. We derive an asymptotic distribution of the estimator, construct a practically implementable confidence interval for the distortion parameter, and illustrate the performance of the interval in a simulation study.

Keywords: Proportional-hazard premium; Proportional-hazard transform; Distortion risk measure; Distortion parameter; Extreme value; Heavy tail; Risk aversion index (search for similar items in EconPapers)
JEL-codes: C13 C14 C16 D81 (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:49:y:2011:i:3:p:325-334

DOI: 10.1016/j.insmatheco.2011.05.001

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