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. © 2012 Elsevier B.V.
Bellini, F., ROSAZZA GIANIN, E. (2012). Haezendonck-Goovaerts risk measures and Orlicz quantiles. INSURANCE MATHEMATICS & ECONOMICS, 51(1), 107-114 [10.1016/j.insmatheco.2012.03.005].
Haezendonck-Goovaerts risk measures and Orlicz quantiles
BELLINI, FABIO;ROSAZZA GIANIN, EMANUELA
2012
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. © 2012 Elsevier B.V.
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