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

Estimating the distortion parameter of the proportional hazards premium for heavy-tailed losses under Lévy-stable regime

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Estimating the distorted parameter in the case of non negative heavy-tailed losses have been treated in Brahimi et al (2011). In this paper, we extend this work to the case of the real heavy-tailed losses.

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Robust estimator of distortion risk premiums for heavy-tailed losses

“…Since we are concerned with with heavy-tailed losses with infinite second moment, then by following Brahimi et al (2011), we assume that γ ∈ (1/2, 1) and ργ ∈ (0, 1) , thus we will work with 1/2 < γ < 1/ρ. Necir and Meraghni (2009) proposed an alternative estimator of (2) and establish its asymptotic normality based on the Weissman's estimator of the high quantile…”

“…The limit behavior was discussed by many authors: Chernoff et al (1967), Stigler (1974), Mason (1981), Jones and Zitikis (2003) (see its Theorem 3.2 in the case that X is not heavy-tailed) and in Brahimi et al (2011) (in heavy-tailed case).…”

Bias-corrected estimation in distortion risk premiums for heavy-tailed losses

“…For recent literature on statistical inference for distortion premiums, we refer to Jones and Zitikis (2003), Jones and Zitikis (2007), Centeno and Andrade (2005), Zitikis (2008a, 2008b), Brazauskas et al (2008), Greselin et al (2009), Necir andMeraghni (2009), Necir and Meraghni (2010), Brahimi et al (2011), Peng et al (2012 and the references therein.…”