Stability properties of Haezendonck–Goovaerts premium principles

Niushan Gao, Cosimo Munari and Foivos Xanthos

Insurance: Mathematics and Economics, 2020, vol. 94, issue C, 94-99

Abstract: We investigate a variety of stability properties of Haezendonck–Goovaerts premium principles on their natural domain, namely Orlicz spaces. We show that such principles always satisfy the Fatou property. This allows to establish a tractable dual representation without imposing any condition on the reference Orlicz function. In addition, we show that Haezendonck–Goovaerts principles satisfy the stronger Lebesgue property if and only if the reference Orlicz function fulfills the so-called Δ2 condition. We also discuss (semi)continuity properties with respect to Φ-weak convergence of probability measures. In particular, we show that Haezendonck–Goovaerts principles, restricted to the corresponding Young class, are always lower semicontinuous with respect to the Φ-weak convergence.

Keywords: Haezendonck–Goovaerts principles; Orlicz spaces; Fatou property; Lebesgue property; ϕ-weak convergence (search for similar items in EconPapers)
JEL-codes: C65 G10 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:94:y:2020:i:c:p:94-99

DOI: 10.1016/j.insmatheco.2020.06.010

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