Generalized Coherent Risk Measures

In this paper we indicate a natural generalization of the notion of the coherent risk measure in some partially ordered normed linear space E, according to the remark that was first made in [9] about the relation between coherent risk measures and coherent valuation bounds. The generalization relies on considering a subspace of assets whose elements are used in order to hedge every financial position under the minimum cost with respect to some spot price functional. This subspace is supposed to be a finite-dimensional cofinal subspace of E or a wedge of E which behaves in the same way. We prove some properties of these risk measures being similar to the ones which hold about coherent risk measures and we give some examples of cofinal subspaces in partially ordered linear spaces. Mathematics Subject Classification: 46B40, 46A40, 91B28, 91B30