Acta Oeconomica Pragensia 2007, 15(4):99-110 | DOI: 10.18267/j.aop.79

Multistage Stochastic Programming via Autoregressive Sequences

Vlasta Kaňková
RNDr. Vlasta Kaňková, CSc. - research fellow; Department of Econometrics, Institute of Information Theory and Automation of the Academy of Sciences of the Czech Republic, Pod vodárenskou věží 4, 182 08 Prague 8, Czech Republic, kankova@utia.cas.cz

Economic activities developing over time are very often influenced simultaneously by a random factor (modeled mostly by a stochastic process) and a "decision" parameter (that has to be chosen according to economic possibilities). Theory of multistage stochastic programming, controlled Markov processes as well as empirical processes can be employed to treat the economic processes. We focus on the multistage stochastic problems with the individual probability constraints and random element following an autoregressive (generally) nonlinear sequence.

Keywords: economic processes, multistage stochastic programming, autoregressive sequences, individual probability constraints
JEL classification: C44

Published: August 1, 2007  Show citation

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Kaňková, V. (2007). Multistage Stochastic Programming via Autoregressive Sequences. Acta Oeconomica Pragensia, 15(4), 99-110. doi: 10.18267/j.aop.79
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    References

    1. BIRGE, J. R.; LOUVEAUX, F. (1997). Introduction to Stochastic Programming. Berlin, Springer-Verlag, 1997.
    2. BIRGE, J. R. (1988). An L-Shaped Method Computer Code for Multistage Stochastic Linear Programs. In Ermoliev, Y. and Wets, R. J. B. (eds.). Numerical Techniques for Stochastic Optimization Problems. Berlin : Springer-Verlag, 1988, pp.255-272. Go to original source...
    3. DUPAČOVÁ, J. (1995). Multistage Stochastic Programs: the State-of-the-Art and Selected Bibliography. Kybernetika, 1995, vol. 31, no. 2, pp. 151-174.
    4. DUPAČOVÁ, J.; HURT, J.; ŠTĚPÁN, J. (2002). Stochastic Modelling in Economics and Finance. Dordrecht : Kluwer, 2002.
    5. DUPAČOVÁ, J.; POPELA, P. (2005). Melt Control: Charge Optimization via Stochastic Programming. In Wallace, S. W.; Ziemba, W. T (eds.) (2005). Applications of Stochastic Programming. Philadelphia, Society for Industrial and Applied Mathematics / Mathematical Programming Society, 2005, pp. 277-298. Go to original source...
    6. CHOVANEC, P. (2004). Multistage Stochastic Programming Problems -Application to Unemployment Problem and Restructuralization (Diploma thesis). Prague : MFF UK, 2004.
    7. ERMOLIEV, Y.; WETS, R. J. B. (eds.) (1988). Numerical Technique for Stochastic Optimization. Berlin : Springer, 1988. Go to original source...
    8. FRAUENDORFER, K.; SCHURLE, M. (2000). Term Structure in Multistage Stochastic Programming: Estimation and Approximation. Annals of Operations Research, 2000, vol. 100, no. 1-4, pp. 189-209. Go to original source...
    9. KAŇKOVÁ, V. (1996). A Note on Multifunction in Stochastic Programming. In Marti, K.; Kall, P. (eds.). Stochastic Programming Methods and Technical Applications. Berlin : Springer, 1996.
    10. KAŇKOVÁ, V. (1998). A Note on Multistage Stochastic Programming. In Proceedings 11th joint Czech-Germany-Slovak Conference. Liberec : University of Technology, pp. 45-52.
    11. KAŇKOVÁ, V. (2002). A Remark on the Analysis of Multistage Stochastic Programs: Markov dependence. Zeitschrift für Angewandte Mathematik und Mechanik, 2002, vol. 82, no. 11-12, pp. 781-793. Go to original source...
    12. KAŇKOVÁ, V. (2005). Multistage Stochastic Decision and Economic Processes. Acta Oeconomica Pragensia, 2005, vol. 13, no. 1, pp. 119-127. Go to original source...
    13. KAŇKOVÁ, V. (2007). Multistage Stochastic Programming Problems; Stability and Approximation. In Waldmann, K.-H.; Stocker, U. M. (eds.). Operations Research Proceedings 2006, Berlin : Springer, 2007, pp. 595-600. Go to original source...
    14. KAŇKOVÁ, V.; HOUDA, M. (2002). A Note on Quantitative Stability and Empirical Estimates in Stochastic Programming. In Leopold-Wildburger, U.; Rendl, F.; Wäscher, G. (eds.). Operations Research Proceedings 2002. Berlin : Springer-Verlag, 2003, pp. 413-418. Go to original source...
    15. KAŇKOVÁ, V.; HOUDA, M. (2006a). Empirical Estimates in Stochastic Programming. In Hušková, M.; Janžura, M. (eds.). Proceedings of Prague Stochastics 2006. Prague : Matfyzpress, 2006, pp. 426-436.
    16. KAŇKOVÁ, V.; HOUDA, M. (2006b). Dependent Samples in Empirical Estimation of Stochastic Programming Problems. Austrian Journal of Statistics, 2006, vol. 35, no. 2-3, pp. 271-279.
    17. KAŇKOVÁ, V.; CHOVANEC, P. (2006). Unemployment Problem via Multistage Stochastic Programming. In Pekár, J.; Lukáčik, M. (eds.). Proceedings of Quantitative methods in Economics (Multiple Criteria Decision making XIII). Bratislava, The Slovak Society for Operations Research / University of Economics in Bratislava, 2006, pp. 69-76.
    18. KAŇKOVÁ, V.; ŠMÍD, M. (2004). A Remark on Approximation in Multistage Stochastic Programming; Markov Dependence. Kybernetika, 2004, vol. 40, no. 5, pp.625-638.
    19. KING, A. J. (1988). Stochastic Programming Problems: Examples from the Literature. In Ermoliev, Y.; Wets, R. J.-B. (eds.). Numerical Techniques for Stochastic Optimization Problems. Berlin : Springer, 1988, pp. 543-567. Go to original source...
    20. KUHN, D. (2005). Generalized Bounds for Convex Multistage Stochastic Programs. Lectures Notes in Economics and Mathematical Systems 548. Berlin : Springer-Verlag, 2005.
    21. NOWAK, M.; RÖMISCH, W. (2000). Stochastic Lagrangian Relaxation Applied to Power Scheduling in Hydro-Termal System Under Uncertainty. Annals of Operation Research, 2000. Vol. 100, pp. 251-272. Go to original source...
    22. PFLUG G. Ch. (2001). Scenario Tree Generation for Multiperiod Financial Optimization by Optimal Discretization. Mathematical Programming, 2001, vol. 89, serie B89, pp. 251-271. Go to original source...
    23. POWEL, W. B.; TOPALOGLU, H. (2003). Stochastic Programming in Transportation and Logistics. In Ruszczynski, A.; Shapiro, A. (eds.). Stochastic Programming, Handbooks in Operations Research and Management Science, vol. 10. Amsterdam : Elsevier, pp. 555-636. Go to original source...
    24. PREKOPA, A. (1995). Stochastic Programming. Budapest : Akadémiai Kiadó and Dordrecht, Kluwer, 1995. Go to original source...
    25. RACHEV, S. T. (1991). Probability Metrics and the Stability of Stochastic Models. New York : Wiley, 1991.
    26. ROMISCH, W.; SCHULZ, R. (1993). Stability of Solutions for Stochastic Programs with Complete Recourse. Mathematics of Operation Research, 1993, vol.18, no. 3, pp. 590-609. Go to original source...
    27. RUSZCZYŇSKI, A. (2003). Decomposition Methods. In Ruszczynski, A.; Shapiro, A. (eds.). Stochastic Programming, Handbooks in Operations Research and Management Science, vol. 10. Amsterdam : Elsevier, 2003, pp. 141-209. Go to original source...
    28. SERFLING, J. R. (1980). Approximation Theorems of Mathematical Statistics. New York : Wiley, 1980. Go to original source...
    29. SHORACK, G. R.; WELLNER, J. A. (1986). Empirical Processes with Applications to Statistics. New York : Wiley, 1986.
    30. ŠMÍD, M. (2004). On Approximation of Stochastic Programming Problems. (Doctoral Thesis). Prague : MFF UK, 2004.
    31. VALLENDER, S. S. (1973). Calculation of the Wasserstein Distance between Probability Distribution on the Line. Theory of Probability and its Applications, 1973, vol. 18, no. 4, pp. 784-786. Go to original source...
    32. WALLACE, S. W.; FLETEN, S. E. (2003). Stochastic Programming Models in Energy. In Ruszczynski, A.; Shapiro, A. (eds.). Stochastic Programming, Handbooks in Operations Research and Management Science, Amsterdam : Elsevier, 2003, vol. 10, pp. 637-677. Go to original source...
    33. WALLACE, S. W; ZIEMBA, W. T (eds.) (2005). Applications of Stochastic Programming. Philadelphia : Society for Industrial and Applied Mathematics / Mathematical Programming Society, 2005. Go to original source...

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