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Trade-off Between Robust Risk Measurement and Market Principles

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  • Hirbod Assa

    (University of Liverpool)

Abstract

Recently, it was shown that coherent risk measures are not robust with respect to changes in large data. On the other hand, in this article, we show that robust risk measures always generate pathological financial positions, Good Deals. This leaves a decision maker with a problem to either choose a robust risk measurement approach in a day-to-day real life decision making or an approach, which can correctly price financial products by considering the market principals such as No Good Deal assumption. In this paper, after stating clearly this problem, we propose a solution by introducing the minimal distribution-invariant modification of the risk measure, which does not produce any Good Deal and also is more robust comparing to the family of coherent risk measures.

Suggested Citation

  • Hirbod Assa, 2015. "Trade-off Between Robust Risk Measurement and Market Principles," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 306-320, July.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:1:d:10.1007_s10957-014-0593-8
    DOI: 10.1007/s10957-014-0593-8
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    References listed on IDEAS

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    1. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    2. Balbás, Alejandro & Balbás, Raquel & Mayoral, Silvia, 2009. "Portfolio choice and optimal hedging with general risk functions: A simplex-like algorithm," European Journal of Operational Research, Elsevier, vol. 192(2), pages 603-620, January.
    3. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Optimization of Convex Risk Functions," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 433-452, August.
    4. Hirbod Assa & Keivan Mallahi Karai, 2013. "Hedging, Pareto Optimality, and Good Deals," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 900-917, June.
    5. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 593-606.
    6. Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2009. "Optimal reinsurance with general risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 374-384, June.
    7. R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, January.
    8. Aleš Černý, 2003. "Generalised Sharpe Ratios and Asset Pricing in Incomplete Markets," Review of Finance, European Finance Association, vol. 7(2), pages 191-233.
    9. Alexander S. Cherny, 2006. "Equilibrium with coherent risk," Papers math/0605051, arXiv.org.
    10. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Post-Print hal-00413729, HAL.
    11. Alexander Schied, 2007. "Optimal investments for risk- and ambiguity-averse preferences: a duality approach," Finance and Stochastics, Springer, vol. 11(1), pages 107-129, January.
    12. Branda, Martin, 2013. "Diversification-consistent data envelopment analysis with general deviation measures," European Journal of Operational Research, Elsevier, vol. 226(3), pages 626-635.
    13. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, Michael, 2006. "Master funds in portfolio analysis with general deviation measures," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 743-778, February.
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    Cited by:

    1. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2016. "Coherent Pricing," INDEM - Working Paper Business Economic Series 22932, Instituto para el Desarrollo Empresarial (INDEM).

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