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Risk Measures in Optimization Problems via Empirical Estimates

Author

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  • Vlasta Kaňková

    (Academy of Sciences of the Czech Republic, Institute of Information Theory and Automation, Department of Econometrics, Prague, Czech Republic)

Abstract

Economic and financial activities are often influenced simultaneously by a decision parameter and a random factor. Since mostly it is necessary to determine the decision parameter without knowledge of the realization of the random element, deterministic optimization problems depending on a probability measure often correspond to such situations. In applications the problem has to be very often solved on the data basis. It means that usually the “underlying” probability measure is replaced by empirical one. Great effort has been made to investigate properties of the corresponding (empirical) estimates; mostly under assumptions of “thin” tails and a linear dependence on the probability measure. The aim of this paper is to focus on the cases when these assumptions are not fulfilled. This happens usually just in economic and financial applications (see, e.g., Mandelbort 2003; Pflug and Römisch 2007; Rachev and Römisch 2002; Shiryaev 1999).

Suggested Citation

  • Vlasta Kaňková, 2013. "Risk Measures in Optimization Problems via Empirical Estimates," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 7(3), pages 162-177, November.
    • Handle: RePEc:fau:aucocz:au2013_162
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    References listed on IDEAS

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    1. Svetlozar T. Rachev & Werner Römisch, 2002. "Quantitative Stability in Stochastic Programming: The Method of Probability Metrics," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 792-818, November.
    2. Vadym Omelchenko, 2012. "Behaviour and convergence of Wasserstein metric in the framework of stable distributions," Bulletin of the Czech Econometric Society, The Czech Econometric Society, vol. 19(30).
    3. Georg Ch Pflug & Werner Römisch, 2007. "Modeling, Measuring and Managing Risk," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6478, June.
    4. Michal Houda & Vlasta Kaňková, 2012. "Empirical Estimates in Economic and Financial Optimization Problems," Bulletin of the Czech Econometric Society, The Czech Econometric Society, vol. 19(29).
    5. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    6. L. Dai & C. H. Chen & J. R. Birge, 2000. "Convergence Properties of Two-Stage Stochastic Programming," Journal of Optimization Theory and Applications, Springer, vol. 106(3), pages 489-509, September.
    7. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    More about this item

    Keywords

    Static stochastic optimization problems; linear and nonlinear dependence; risk measures; thin and heavy tails; Wasserstein metric; L1 norm; empirical distribution function;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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