Acta Oeconomica Pragensia 2005, 13(1):128-134 | DOI: 10.18267/j.aop.145

Using Metrics in Stability of Stochastic Programming Problems

Michal Houda
Mgr. Michal Houda - student of doctoral study; Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 3, 121 16 Prague 2, houda@karlin.mff.cuni.cz

Optimization techniques enter often as a mathematical tool into many economic applications. In these models, uncertainty is modelled via probability distribution that is approximated or estimated in real cases. Then we ask for a stability of solutions with respect to changes in the probability distribution. The work illustrates one of possible approaches (using probability metrics), underlying numerical challenges and a backward glance to economical interpretation.

Keywords: stochastic programming, quantitative stability, Wasserstein metrics, Kolmogorov metrics, simulation study
JEL classification: C44

Published: March 1, 2005  Show citation

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Houda, M. (2005). Using Metrics in Stability of Stochastic Programming Problems. Acta Oeconomica Pragensia13(1), 128-134. doi: 10.18267/j.aop.145
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References

  1. BIRGE, J. R. - LOUVEAUX, F. (1997): Introduction to Stochastic Programming. New York, Springer-Verlag.
  2. HOUDA, M. (2002): Probability metrics and the stability of stochastic programs with recourse. Bulletin of the Czech Econometric Society, vol. 9, issue 17, pp. 65-77.
  3. HOUDA, M. (2004): Wasserstein metrics and empirical distributions in stability of stochastic programs. In Lukacik M. (ed.): Proceedings of the International Conference Quantitative Methods in Economics (Multiple Criteria Decision Making XII). Bratislava, University of Economics, pp. 71-77.
  4. KALL, P. (1976): Stochastic Linear Programming. Berlin, Springer-Verlag. Go to original source...
  5. KANKOVA, V. - HOUDA, M. (2002): A note on quantitative stability and empirical estimates in stochastic programming. In Leopold-Wildburger, U., Rendl, F., Washer, G. (eds.): Operations Research Proceedings 2002. Heidelberg, Springer-Verlag, pp. 413-418. Go to original source...
  6. RACHEV, S. T. (1991): Probability Metrics and the Stability of Stochastic Models. Chichester, Wiley.
  7. ROMISCH, W. (2003): Stability of Stochastic Programming Problems. In Ruszczynski, A., Shapiro, A. (eds.): Stochastic Programming, Handbooks in Operations Research and Management Science, vol. 10. Amsterdam, Elsevier, pp. 483-554. Go to original source...
  8. SHORACK, G. R. - WELLNER, J. A. (1986): Empirical Processes with Applications to Statistics. New York, John Wiley&Sons.
  9. ZOLOTAREV, V. M. (1983): Probability metrics. Theory of Probability and its Applications, vol. 28, pp. 278-302. Go to original source...

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