Risk measures on ordered non-reflexive Banach spaces

This work is devoted to the study of coherent and convex risk measure on non-reflexive Banach spaces. An extension of dual representation and continuity results which hold in the case of reflexive spaces is established in this paper for the class of non-reflexive Banach spaces. This study also relies on the fact that the riskless bond is replaced by some numeraire asset which defines a base on the cone of the spot-price functionals.