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.
Author: | Hans Föllmer, Irina Penner |
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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 |