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Conditional and Dynamic Convex Risk Measures

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Author Info
Kai Detlefsen
Giacomo Scandolo
Abstract

We extend the definition of a convex risk measure to a conditional framework where additional information is available. We characterize these risk measures through the associated acceptance sets and prove a representation result in terms of conditional expectations. As an example we consider the class of conditional entropic risk measures. A new regularity property of conditional risk measures is defined and discussed. Finally we introduce the concept of a dynamic convex risk measure as a family of successive conditional convex risk measures and characterize those satisfying some natural time consistency properties.

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Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2005-006.

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Length: 23 pages
Date of creation: Feb 2005
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Handle: RePEc:hum:wpaper:sfb649dp2005-006

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Related research
Keywords: Conditional convex risk measure; robust representation; regularity; entropic risk measure; dynamic convex risk measure; time consistency;

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Find related papers by JEL classification:
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July. [Downloadable!] (restricted)
  2. Frank Riedel, 2003. "Dynamic Coherent Risk Measures," Working Papers 03004, Stanford University, Department of Economics. [Downloadable!]
  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. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Samuel N. Cohen & Robert J. Elliott, 2008. "Comparisons for Backward Stochastic Differential Equations on Markov Chains and related No-Arbitrage Conditions," Quantitative Finance Papers 0810.0055, arXiv.org. [Downloadable!]
  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!]
  3. Nicole El Karoui & Claudia Ravanelli, 2007. "Cash Sub-additive Risk Measures and Interest Rate Ambiguity," Quantitative Finance Papers 0710.4106, arXiv.org. [Downloadable!]
  4. Jocelyne Bion-Nadal, 2007. "Bid-Ask Dynamic Pricing in Financial Markets with Transaction Costs and Liquidity Risk," Quantitative Finance Papers math/0703074, arXiv.org. [Downloadable!]
  5. Jocelyne Bion-Nadal, 2006. "Time Consistent Dynamic Risk Processes, Cadlag Modification," Quantitative Finance Papers math/0607212, arXiv.org. [Downloadable!]
  6. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Dynamic Variational Preferences," Carlo Alberto Notebooks 1, Collegio Carlo Alberto. [Downloadable!]
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