Erratum: Coherent and convex risk measures for unbounded càdlàg processes
type: Item
instance of: scholarly article
title: Erratum: Coherent and convex risk measures for unbounded càdlàg processes
zbMATH Open document ID: 1124.91039
author: Patrick Cheridito
author: Michael Kupper
author: Freddy Delbaen
published in: Finance and Stochastics
publication date: 2006-12-08T00:00:00Z
review text: 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.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 60G07
Mathematics Subject Classification ID: 52A07
Mathematics Subject Classification ID: 46A55
Mathematics Subject Classification ID: 46A20
zbMATH DE Number: 5079148
zbMATH Keywords: coherent risk measures
zbMATH Keywords: convex monetary risk measures
zbMATH Keywords: coherent utility functional
zbMATH Keywords: concave monetary utility functional
zbMATH Keywords: unbounded càdlàg processes
zbMATH Keywords: extension of risk measures
MaRDI profile type: Publication
full work available at URL: s00780-006-0017-1
OpenAlex ID: W1971575668
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DOI: 10.1007/S00780-006-0017-1
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description: scientific article; zbMATH DE number 5079148