Convex risk measures and the dynamics of their penalty functions

Please always quote using this URN:urn:nbn:de:0296-matheon-3369
  • We study various properties of a dynamic convex risk measure for bounded random variables which describe the discounted terminal values of financial positions. In particular we characterize time-consistency by a joint supermartingale property of the risk measure and its penalty function. Moreover we discuss the limit behavior of the risk measure in terms of asymptotic safety and of asymptotic precision, a property which may be viewed as a non-linear analogue of martingale convergence. These results are illustrated by the entropic dynamic risk measure.

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Metadaten
Author:Hans Föllmer, Irina Penner
URN:urn:nbn:de:0296-matheon-3369
Referee:Peter Imkeller
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2006/03/05
Release Date:2006/03/05
Tag:
Institute:Humboldt-Universität zu Berlin
Technische Universität Berlin
MSC-Classification:91-XX GAME THEORY, ECONOMICS, SOCIAL AND BEHAVIORAL SCIENCES / 91Bxx Mathematical economics (For econometrics, see 62P20) / 91B16 Utility theory
91-XX GAME THEORY, ECONOMICS, SOCIAL AND BEHAVIORAL SCIENCES / 91Bxx Mathematical economics (For econometrics, see 62P20) / 91B30 Risk theory, insurance
Preprint Number:327
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