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Dynamic monetary risk measures for bounded discrete-time processes

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Author Info
Patrick Cheridito
Freddy Delbaen
Michael Kupper
Abstract

We study time-consistency questions for processes of monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of monetary risk measures time-consistent if it assigns to a process of financial values the same risk irrespective of whether it is calculated directly or in two steps backwards in time, and we show how this property manifests itself in the corresponding process of acceptance sets. For processes of coherent and convex monetary risk measures admitting a robust representation with sigma-additive linear functionals, we give necessary and sufficient conditions for time-consistency in terms of the representing functionals.

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File URL: http://arxiv.org/abs/math/0410453
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number math/0410453.

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Date of creation: Oct 2004
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Handle: RePEc:arx:papers:math/0410453

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  1. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November. [Downloadable!] (restricted)
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  2. Wang, Tan, 2003. "Conditional preferences and updating," Journal of Economic Theory, Elsevier, vol. 108(2), pages 286-321, February. [Downloadable!] (restricted)
  3. Berend Roorda & J. M. Schumacher & Jacob Engwerda, 2005. "Coherent Acceptability Measures In Multiperiod Models," Mathematical Finance, Blackwell Publishing, vol. 15(4), pages 589-612. [Downloadable!] (restricted)
  4. Marco Frittelli, 2000. "Introduction to a theory of value coherent with the no-arbitrage principle," Finance and Stochastics, Springer, vol. 4(3), pages 275-297. [Downloadable!] (restricted)
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  1. Alexander Schied, 2005. "Optimal Investments for Risk- and Ambiguity-Averse Preferences: A Duality Approach," SFB 649 Discussion Papers SFB649DP2005-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Aug 2006. [Downloadable!]
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  2. Castaneda, Pablo, 2006. "Long Term Risk Assessment in a Defined Contribution Pension System," MPRA Paper 3347, University Library of Munich, Germany, revised 30 Apr 2007. [Downloadable!]
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