Abstracts

In this article we study the construction of coherent or convex risk measures defined either on a Orlicz heart, either on an Orlicz space, with respect to a Young loss function. The Orlicz heart is taken as a subset of $L^{0}(\omega, \mathcal{F}, \mu)$ endowed with the pointwise partial ordering. We define set-valued risk measures related to this partial ordering. We also derive monetary risk measures both by this class of set-valued risk measures and by the class of set-valued risk measures which has the properties mentioned in Jouini et al. (2004) and we compare their properties. We also use random measures related to heavy-tailed distributions in order to define monetary risk measures on Orlicz spaces, whose properties are also compared to the previous ones. The final part of the article is devoted to portfolio optimization problems which use these risk measures in practice and moreover with elements of their statistics.