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arXiv · 1909.10735

Stability properties of Haezendonck-Goovaerts premium principles

Niushan Gao·Cosimo Munari·Foivos Xanthos
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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 $Δ_2$ 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.

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Niushan Gao, Cosimo Munari, Foivos Xanthos. 2020-08-12. Stability properties of Haezendonck-Goovaerts premium principles. https://arxiv.org/abs/1909.10735

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