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Empirical Estimates in Economic and Financial Optimization Problems

Author

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  • Michal Houda

    ()

  • Vlasta Kaňková

    ()

Abstract

Many applications from economic and financial practice lead to optimization problems depending on a probability measure. A complete knowledge of the "underlying" measure is a necessary assumption to determine an exact optimal solution and an exact optimal value. Since this condition is not usually fulfilled, the solution is often determined on an empirical data base. Estimates of the optimal value and the optimal solution sets can be obtained by this approach only. Many efforts has been paid to the investigation of the above mentioned estimates. Especially the consistency and the convergence rate have been investigated. However, it was mostly done for "classical" problems and "underlying" distributions with "thin" tails. The aim of this paper is to analyze these estimates from the point of the distribution tails, generally. To this end, first, we recall some known results. Furthermore, we recall stability results based on the Wasserstein metric corresponding to L1 norm (see e.g. Kan (2006b), Kan (2006a)) and employ them to the case of "heavy" tails. Results based on a simulation technique complete our investigation.

Suggested Citation

  • 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).
  • Handle: RePEc:czx:journl:v:19:y:2012:i:29:id:195
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    File URL: http://ces.utia.cas.cz/bulletin/index.php/bulletin/article/view/195
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    Cited by:

    1. Vlasta Kaňková, 2016. "A remark on multiobjective stochastic optimization via strongly convex functions," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 24(2), pages 309-333, June.
    2. 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.

    More about this item

    Keywords

    stochastic programming; empirical estimates; moment generating function; stability; Wasserstein metric; L1 norm; Lipschitz property; consistence; convergence rate; normal distribution; Pareto distribution; Weibull distribution; distribution tails.;

    JEL classification:

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

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