Approximations for probability distributions and stochastic optimization problems

International Series in Operations Research and Management Science

Volumn 163, Issue , 2011, Pages 343-387

  Pflug, Georg Ch ^a   Pichler, Alois ^b  

^a UNIVERSITY OF VIENNA   (Austria)

^b NONE

Author keywords

Nested distributions; Optimal discretizations; Probability distances; Scenario generation; Scenario trees

Indexed keywords

EID: 84955304233     PISSN: 08848289     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-1-4419-9586-5_15     Document Type: Chapter

References (20)

1. Z. Drezner and H.W. Hamacher. Facility Location: Applications and Theory. Springer, New York, NY, 2002.
2. J. Dupacova. Stability and sensitivity analysis for stochastic programming. Annals of Operations Research, 27:115-142, 1990.
3. Richard Durrett. Probability: Theory and Examples. Duxbury Press, Belmont, CA, second edition, 1996.
4. A. Gibbs and F.E. Su. On choosing and bounding probability metrics. International Statistical Review, 70(3):419-435, 2002.
5. S. Graf and H. Luschgy. Foundations of Quantization for Probability Distributions. Lecture Notes in Math. 1730. Springer, Berlin, 2000.
6. H. Heitsch and W. Roemisch. Scenario reduction algorithms in stochastic programming. Computational Optimization and Applications, 24:187-206, 2003.
7. H. Heitsch, W. Roemisch, and C. Strugarek. Stability of multistage stochastic programs. SIAM Journal on Optimization, 17:511-525, 2006.
8. C.C. Heyde. On a property of the lognormal distribution. Journal of Royal Statistical Society Series B, 25(2):392-393, 1963.
9. R. Hochreiter and G. C. Pflug. Financial scenario generation for stochastic multi-stage decision processes as facility location problems. Annals of Operation Research, 152(1):257-272, 2007.
10. K. Hoyland and S.W. Wallace. Generating scenario trees for multistage decision problems. Management Science, 47:295-307, 2001.
11. S. Na and D. Neuhoff. Bennett's integral for vector quantizers. IEEE Transactions on Information Theory, 41(4):886-900, 1995.
12. H. Niederreiter. Random Number Generation and Quasi-Monte Carlo Methods, volume 23. CBMS-NSF Regional Conference Series in Applied Math., Soc. Industr. Applied Math., Philadelphia, PA, 1992.
13. T. Pennanen. Epi-convergent discretizations of multistage stochastic programs via integration quadratures. Mathematical Programming, 116:461-479, 2009.
14. G. C. Pflug. Scenario tree generation for multiperiod financial optimization by optimal discretization. Mathematical Programming, Series B, 89:251-257, 2001.
15. G. C. Pflug. Version-independence and nested distributions in multistage stochastic optimization. SIAM Journal on Optimization, 20(3):1406-1420, 2009.
16. S.T. Rachev and W. Roemisch. Quantitative stability in stochastic programming: The method of probability metrics. Mathematics of Operations Research, 27(4):792-818, 2002.
17. S.T. Rachev. Probability Metrics and the Stability of Stochastic Models. Wiley, New York, NY, 1991.
18. S.S. Vallander. Calculation of the Wasserstein distance between probability distributions on the line. Theor. Prob. Appl., 18:784-786, 1973.
19. C. Villani. Optimal Transport. Springer, Berlin, Heidelberg, 2008.
20. A. Weber. Theory of the Location of Industries. The University of Chicago Press, Chicago, IL 1929.