IDEAS home Printed from https://ideas.repec.org/a/fau/aucocz/au2013_162.html
   My bibliography  Save this article

Risk Measures in Optimization Problems via Empirical Estimates

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://auco.cuni.cz/mag/article/download/id/151/type/attachment
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. repec:czx:journl:v:19:y:2012:i:30:id:205 is not listed on IDEAS
    3. Georg Ch Pflug & Werner Römisch, 2007. "Modeling, Measuring and Managing Risk," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6478, October.
    4. repec:czx:journl:v:19:y:2012:i:29:id:195 is not listed on IDEAS
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vlasta Kaňková, 2024. "Stochastic optimization problems with nonlinear dependence on a probability measure via the Wasserstein metric," Journal of Global Optimization, Springer, vol. 90(3), pages 593-617, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alois Pichler, 2013. "Premiums And Reserves, Adjusted By Distortions," Papers 1304.0490, arXiv.org.
    2. Branda, Martin, 2013. "Diversification-consistent data envelopment analysis with general deviation measures," European Journal of Operational Research, Elsevier, vol. 226(3), pages 626-635.
    3. D. Kuhn, 2009. "Convergent Bounds for Stochastic Programs with Expected Value Constraints," Journal of Optimization Theory and Applications, Springer, vol. 141(3), pages 597-618, June.
    4. Justo Puerto & Moises Rodr'iguez-Madrena & Andrea Scozzari, 2019. "Location and portfolio selection problems: A unified framework," Papers 1907.07101, arXiv.org.
    5. Martin Herdegen & Cosimo Munari, 2023. "An elementary proof of the dual representation of Expected Shortfall," Papers 2306.14506, arXiv.org.
    6. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2002. "CVaR models with selective hedging for international asset allocation," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1535-1561, July.
    7. Jing-Rung Yu & Wan-Jiun Paul Chiou & Jian-Hong Yang, 2017. "Diversification benefits of risk portfolio models: a case of Taiwan’s stock market," Review of Quantitative Finance and Accounting, Springer, vol. 48(2), pages 467-502, February.
    8. Albrecht, Peter, 2003. "Risk measures," Papers 03-01, Sonderforschungsbreich 504.
    9. Zhi-Long Dong & Fengmin Xu & Yu-Hong Dai, 2020. "Fast algorithms for sparse portfolio selection considering industries and investment styles," Journal of Global Optimization, Springer, vol. 78(4), pages 763-789, December.
    10. Kouaissah, Noureddine, 2021. "Using multivariate stochastic dominance to enhance portfolio selection and warn of financial crises," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 480-493.
    11. Adabi Firouzjaee , Bagher & Mehrara , Mohsen & Mohammadi , Shapour, 2014. "Optimal Portfolio Selection for Tehran Stock Exchange Using Conditional, Partitioned and Worst-case Value at Risk Measures," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 9(1), pages 1-30, October.
    12. Yu, Jing-Rung & Paul Chiou, Wan-Jiun & Hsin, Yi-Ting & Sheu, Her-Jiun, 2022. "Omega portfolio models with floating return threshold," International Review of Economics & Finance, Elsevier, vol. 82(C), pages 743-758.
    13. Huifu Xu & Dali Zhang, 2012. "Monte Carlo methods for mean-risk optimization and portfolio selection," Computational Management Science, Springer, vol. 9(1), pages 3-29, February.
    14. Martin Herdegen & Nazem Khan, 2020. "Mean-$\rho$ portfolio selection and $\rho$-arbitrage for coherent risk measures," Papers 2009.05498, arXiv.org, revised Jul 2021.
    15. Bellini Fabio & Rosazza Gianin Emanuela, 2008. "Optimal portfolios with Haezendonck risk measures," Statistics & Risk Modeling, De Gruyter, vol. 26(2), pages 89-108, March.
    16. Frank Fabozzi & Dashan Huang & Guofu Zhou, 2010. "Robust portfolios: contributions from operations research and finance," Annals of Operations Research, Springer, vol. 176(1), pages 191-220, April.
    17. Prékopa, András & Lee, Jinwook, 2018. "Risk tomography," European Journal of Operational Research, Elsevier, vol. 265(1), pages 149-168.
    18. Akhter Mohiuddin Rather & V. N. Sastry & Arun Agarwal, 2017. "Stock market prediction and Portfolio selection models: a survey," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 558-579, September.
    19. Salo, Ahti & Doumpos, Michalis & Liesiö, Juuso & Zopounidis, Constantin, 2024. "Fifty years of portfolio optimization," European Journal of Operational Research, Elsevier, vol. 318(1), pages 1-18.
    20. Lagos, Guido & Espinoza, Daniel & Moreno, Eduardo & Vielma, Juan Pablo, 2015. "Restricted risk measures and robust optimization," European Journal of Operational Research, Elsevier, vol. 241(3), pages 771-782.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fau:aucocz:au2013_162. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Lenka Stastna (email available below). General contact details of provider: https://edirc.repec.org/data/icunicz.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.