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Dynamic risk measures

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  • Beatrice Acciaio
  • Irina Penner
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    Abstract

    This paper gives an overview of the theory of dynamic convex risk measures for random variables in discrete time setting. We summarize robust representation results of conditional convex risk measures, and we characterize various time consistency properties of dynamic risk measures in terms of acceptance sets, penalty functions, and by supermartingale properties of risk processes and penalty functions.

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    File URL: http://arxiv.org/pdf/1002.3794
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    Paper provided by arXiv.org in its series Papers with number 1002.3794.

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    Date of creation: Feb 2010
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    Handle: RePEc:arx:papers:1002.3794

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    Web page: http://arxiv.org/

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    1. A. Jobert & L. C. G. Rogers, 2007. "Valuations and dynamic convex risk measures," Papers 0709.0232, arXiv.org.
    2. Jocelyne Bion-Nadal, 2008. "Dynamic risk measures: Time consistency and risk measures from BMO martingales," Finance and Stochastics, Springer, vol. 12(2), pages 219-244, April.
    3. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    4. Frank Riedel, 2003. "Dynamic Coherent Risk Measures," Working Papers 03004, Stanford University, Department of Economics.
    5. Sina Tutsch, 2008. "Update rules for convex risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 833-843.
    6. Michael Mania & Martin Schweizer, 2005. "Dynamic exponential utility indifference valuation," Papers math/0508489, arXiv.org.
    7. Roorda, Berend & Schumacher, J.M., 2007. "Time consistency conditions for acceptability measures, with an application to Tail Value at Risk," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 209-230, March.
    8. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    9. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. Beatrice Acciaio & Hans Foellmer & Irina Penner, 2010. "Risk assessment for uncertain cash flows: Model ambiguity, discounting ambiguity, and the role of bubbles," Papers 1002.3627, arXiv.org.
    11. Marco Frittelli & Giacomo Scandolo, 2006. "Risk Measures And Capital Requirements For Processes," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 589-612.
    12. Föllmer Hans & Penner Irina, 2006. "Convex risk measures and the dynamics of their penalty functions," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 36, July.
    13. Berend Roorda & J. M. Schumacher & Jacob Engwerda, 2005. "Coherent Acceptability Measures In Multiperiod Models," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 589-612.
    14. Stefan Weber, 2006. "Distribution-Invariant Risk Measures, Information, And Dynamic Consistency," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 419-441.
    15. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
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