Risk measures in ordered normed linear spaces with non-empty cone-interior

Abstract

In this paper, we use tools from the theory of partially ordered normed linear spaces, especially the bases of cones. This work extends the well-known results for convex and coherent risk measures. Its linchpin consists in the replacement of the riskless bond by some interior point in the cone of the space of risks, which stands as the alternative numeraire.Base of a cone Well-based cones Numeraire asset Coherent and convex risk measures Representability of risk measures