Abstract We deal with the problem of the practical use of Haezendonck risk measures (see Haezendonck and Goovaerts [8], Goovaerts et al. [7], Bellini and Rosazza Gianin [4]) in portfolio optimization. We first analyze the properties of the natural estimators of Haezendonck risk measures by means...

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...

We study the Haezendonck risk measure (introduced by [Haezendonck, J., Goovaerts, M., 1982. A new premium calculation principle based on Orlicz norms. Insurance: Mathematics and Economics 1, 41-53] and by [Goovaerts, M.J., Kaas, R., Dhaene, J., Tang, Q., 2003. A unified approach to generate risk...

Scaled and Studentized statistics are encountered frequently, and they often play a decisive role in statistical inference and testing. For instance, taking the sample mean vector X̄=∑j=1NXj/N and the sample covariance matrix S=∑j=1N(Xj−X̄)(Xj−X̄)′/(N−1) for an iid sample...