Erratum: Coherent and convex risk measures for unbounded càdlàg processes
This paper is the publisher's erratum to the one published incorrectly due to the typesetting process in Finance Stoch. 9, No. 3, 369--387 (2005; Zbl 1092.91039). In the article the authors prove a theorem which shows that the requirement that coherent convex risk measures are real valued is too restrictive and it is better to let them take values in \((-\infty,\infty]\). This leads to the definition of coherent and convex monetary risk measures on \(\mathcal{R}^0\). The paper main result gives a characterization of coherent and convex monetary risk measures on \(\mathcal R^\infty\) that can be extended to coherent and convex risk measures on \(\mathcal R^0\). Two examples of coherent and convex risk measures on \(\mathcal R^0\) are given. The first one is related to the Cramér-Lundberg approach to measuring the risk of an insurance company. The second one is motivated by results of the authors [Stochastic Processes Appl. 112, No. 1, 1--22 (2004; Zbl 1114.91047)], where time consistency properties of dynamic risk measures that depend on one-dimensional random variables are studied.
scientific article; zbMATH DE number 5079148
scientific article