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Convex measures of risk and trading constraints

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Author Info
Hans Föllmer (Institut für Mathematik, Humboldt-Universität, Unter den Linden 6, 10099 Berlin, Germany Manuscript)
Alexander Schied (Institut für Mathematik, Humboldt-Universität, Unter den Linden 6, 10099 Berlin, Germany Manuscript)

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Abstract

We introduce the notion of a convex measure of risk, an extension of the concept of a coherent risk measure defined in Artzner et al. (1999), and we prove a corresponding extension of the representation theorem in terms of probability measures on the underlying space of scenarios. As a case study, we consider convex measures of risk defined in terms of a robust notion of bounded shortfall risk. In the context of a financial market model, it turns out that the representation theorem is closely related to the superhedging duality under convex constraints.

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Publisher Info
Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 6 (2002)
Issue (Month): 4 ()
Pages: 429-447
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Handle: RePEc:spr:finsto:v:6:y:2002:i:4:p:429-447

Note: received: December 2000; final version received: January 2002
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Related research
Keywords: Risk measure convex measure of risk shortfall trading constraints efficient hedging

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Find related papers by JEL classification:
G18 - Financial Economics - - General Financial Markets - - - Government Policy and Regulation
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
C60 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - General
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis

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  1. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146. [Downloadable!] (restricted)
  2. H. Föllmer & D. Kramkov, . "Optional decompositions under constraints," Sonderforschungsbereich 373 1997-31, Humboldt Universitaet Berlin.
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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.)

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  2. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Convex Risk Functions," Risk and Insurance 0404001, EconWPA, revised 08 Oct 2005. [Downloadable!]
  3. Damir Filipovic, 2007. "Optimal Numeraires for Risk Measures," Research Paper Series 187, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  4. Ignacio Cascos & Ilya Molchanov, 2006. "Multivariate Risks And Depth-Trimmed Regions," Statistics and Econometrics Working Papers ws063815, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
  5. Renato Pelessoni & Paolo Vicig, 2003. "Convex Imprecise Previsions for Risk Measurement," Risk and Insurance 0309001, EconWPA. [Downloadable!]
  6. Alejandro Balbas & Esperanza H. Montagut & Maria Jose Perez Fructuoso, 2004. "Hedging bond portfolios versus infinitely many ranked factors of risk," Business Economics Working Papers wb043312, Universidad Carlos III, Departamento de Economía de la Empresa. [Downloadable!]
  7. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  8. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Risk Measures," Risk and Insurance 0407002, EconWPA. [Downloadable!]
  9. Matos, Joao Amaro de & Lacerda, Ana, 2006. "Equilibrium Bid-Ask Spread of European Derivatives in Dry Markets," FEUNL Working Paper Series wp480, Universidade Nova de Lisboa, Faculdade de Economia. [Downloadable!]
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  12. 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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  14. Ignacio Cascos & Ilya Molchanov, 2007. "Multivariate risks and depth-trimmed regions," Finance and Stochastics, Springer, vol. 11(3), pages 373-397, July. [Downloadable!] (restricted)
  15. Imen Bentahar, 2006. "Tail Conditional Expectation for vector-valued Risks," SFB 649 Discussion Papers SFB649DP2006-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  16. 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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  19. Rustam Ibragimov, 2004. "Shifting paradigms: on the robustness of economic models to heavy-tailedness assumptions," Econometric Society 2004 Latin American Meetings 105, Econometric Society. [Downloadable!]
  20. Piotr Jaworski, 2006. "On a subjective approach to risk measurement," Quantitative Finance, Taylor and Francis Journals, vol. 6(6), pages 495-511, December. [Downloadable!] (restricted)
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