On stability of multistage stochastic programs

SIAM Journal on Optimization

Volumn 19, Issue 2, 2008, Pages 952-968

  Küchler, Christian ^a  

^a HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Multistage; Probability metrics; Stability; Stochastic programming

Indexed keywords

CONDITIONAL DISTRIBUTION; DISCRETIZATION; LIPSCHITZ; MULTISTAGE; OPTIMAL VALUES; PROBABILITY METRICS; QUANTITATIVE STABILITY; STABILITY RESULTS; STOCHASTIC PROCESS;

STABILITY; STOCHASTIC PROGRAMMING;

RANDOM PROCESSES;

EID: 67649510619     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/070690365     Document Type: Article

References (20)

1. V. BALLY, G. PAGÈS, AND J. PRINTEMS, A quantization tree method for pricing and hedging multidimensional American options, Math. Finance, 15 (2005), pp. 119-168.
2. K. BARTY, Contributions à la discrétisation des contraintes de mesurabίlité pour les problèmes d'optimisation stochastique, Ph.D. thesis, École Nationale des Ponts et Chaussées, Paris, 2004.
3. J. BlRGE AND F. LOUVEAUX, Introduction to Stochastic Programming, Springer Series in Operations Research, Springer-Verlag, Berlin, 1997.
4. R. DOBRUSHIN, Central limit theorem for non-stationary Markov chains I., Teor. Veroyatnost. i Primenen., 1 (1956), pp. 72-89.
5. E. DYNKIN, Markov Processes, Springer, Berlin, 1965.
6. I. EVSTIGNEEV, Measurable selection and dynamic programming, Math. Oper. Res., 1 (1976), pp. 267-272.
7. H. HEITSCH AND W. RÖMISCH, Scenario tree modeling for multistage stochastic programs, Math. Program., 2008, to appear.
8. H. HEITSCH, W. RÖMISCH, AND C. STRUGAREK, Stability of multistage stochastic programs, SIAM J. Optim., 17 (2006), pp. 511-525.
9. R. HOCHREITER AND G. PFLUG, Financial scenario generation for stochastic multi-stage decision processes as facility location problems, Ann. Oper. Res., 152 (2007), pp. 257-272.
10. K. HøYLAND AND S. WALLACE, Generating scenario trees for multistage decision problems, Management Science, 47 (2001), pp. 295-307.
11. D. KUHN, Generalized bounds for convex multistage stochastic programs, Lecture Notes in Econ. Math. Systems 548, Springer, Berlin, 2005.
12. R. MIRKOV AND G. PFLUG, Tree approximations of dynamic stochastic programs, SIAM J. Optim., 18 (2007), pp. 1082-1105.
13. T. PENNANEN, Epί-convergent discretizations of multistage stochastic programs, Math. Oper. Res., 30 (2005), pp. 245-256.
14. T. PENNANEN, Epi-convergent discretizations of multistage stochastic programs via integration quadratures, Math. Program., 116 (2009), pp. 461-479.
15. S. RACHEV, Probability Metrics and the Stability of Stochastic Models, Wiley, Chichester, 1991.
16. R. RcCKAFELLAR AND R. J.-B. WETS, Continuous Versus Measurable Recourse in N-Stage Stochastic Programming, J. Math. Anal. Appl., 48 (1974), pp. 836-859.
17. R. ROCKAFELLAR AND R. J.-B. WETS, Variational Analysis, Springer-Verlag, Berlin, 1998.
18. W. RÖMISCH, Stability of Stochastic Programming Problems, Chap. 8 (2003), pp. 483-554, Vol. 10 of [19].
19. A. RUSZCZYÑSKI AND A. SHAPIRO, EDS., Stochastic programming, Handbooks Oper. Res. Management Sci. 10, Elsevier, Amsterdam, 2003.
20. A. SHAPIRO, Inference of statistical bounds for multistage stochastic programming problems, Math. Methods Oper. Res., 58 (2003), pp. 57-68.