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Haezendonck–Goovaerts risk measures and Orlicz quantiles

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  • Bellini, Fabio
  • Rosazza Gianin, Emanuela

Abstract

In this paper, we study the well-known Haezendonck–Goovaerts risk measures on their natural domain, that is on Orlicz spaces and, in particular, on Orlicz hearts. We provide a dual representation as well as the optimal scenario in such a representation and investigate the properties of the minimizer xα∗ (that we call Orlicz quantile) in the definition of the Haezendonck–Goovaerts risk measure. Since Orlicz quantiles fail to satisfy an internality property, bilateral Orlicz quantiles are also introduced and analyzed.

Suggested Citation

  • Bellini, Fabio & Rosazza Gianin, Emanuela, 2012. "Haezendonck–Goovaerts risk measures and Orlicz quantiles," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 107-114.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:1:p:107-114
    DOI: 10.1016/j.insmatheco.2012.03.005
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    References listed on IDEAS

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    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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