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Stability properties of Haezendonck–Goovaerts premium principles

Author

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  • Gao, Niushan
  • Munari, Cosimo
  • Xanthos, Foivos

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.

Suggested Citation

  • Gao, Niushan & Munari, Cosimo & Xanthos, Foivos, 2020. "Stability properties of Haezendonck–Goovaerts premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 94-99.
    • Handle: RePEc:eee:insuma:v:94:y:2020:i:c:p:94-99
    DOI: 10.1016/j.insmatheco.2020.06.010
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    More about this item

    Keywords

    Haezendonck–Goovaerts principles; Orlicz spaces; Fatou property; Lebesgue property; ϕ-weak convergence;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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