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Stability properties of Haezendonck–Goovaerts premium principles


Gao, Niushan; Munari, Cosimo; Xanthos, Foivos (2020). Stability properties of Haezendonck–Goovaerts premium principles. Insurance: Mathematics and Economics, 94:94-99.

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 ∆2 conditions. We also discuss (semi)continuity properties with respect toΦ-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.

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 ∆2 conditions. We also discuss (semi)continuity properties with respect toΦ-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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Economics and Econometrics
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Scope:Discipline-based scholarship (basic research)
Language:English
Date:2020
Deposited On:15 Oct 2020 14:39
Last Modified:23 Jun 2024 01:43
Publisher:Elsevier
ISSN:0167-6687
OA Status:Closed
Publisher DOI:https://doi.org/10.1016/j.insmatheco.2020.06.010
Related URLs:https://doi.org/10.1016/j.insmatheco.2020.06.010
Other Identification Number:merlin-id:19871
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