Skip to main content
SpringerLink
Log in

Testing the structure of multistage stochastic programs

  • Original Paper
  • Published:
Computational Management Science Aims and scope Submit manuscript

Abstract

A fixed topology of stages and/or a fixed branching scheme are common assumptions for applications and numerical solution of scenario based multistage stochastic programs. Using contamination technique to test this structure, we extend the results of Dupačová (Contamination for multistage stochastic programs. In: Hušková M, Janžura M (eds) Prague stochastics. Matfyzpress, Praha, pp 91–101, 2006a) to stochastic programs with multistage polyhedral risk objectives. The ideas are exemplified by bond portfolio management problems and complemented by illustrative numerical results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bertocchi M, Dupačová J, Moriggia V (2006a) Bond portfolio management via stochastic programming. In: Ziemba WT, Zenios SA (eds.) Handbook of Asset & Liability Management. Elsevier, pp. 306–336

  • Bertocchi M, Dupačová J, Moriggia V (2006b) Horizon and stages in applications of stochastic programming in finance. Ann Oper Res 142: 63–78

    Article  Google Scholar 

  • Black F, Derman E, Toy W (1990) A one-factor model of interest rates and its application to treasury bond options. Financial Analysts J., Jan./Feb., pp 33–39

  • Blomwall J, Shapiro A (2007) Solving multistage asset investment problems by the sample average approximation method. Math Program, Ser B 108: 571–595

    Article  Google Scholar 

  • Danskin JM (1967) Theory of Max-Min. Econometrics and Operations Research 5, Springer

  • Dempster MAH et al (2000) Planning logistics operations in the oil industry. J of ORS 51: 1271–1288

    Google Scholar 

  • Dempster MAH, Thompson GWP (2002) Dynamic portfolio replication using stochastic programming. In: Dempster MAH (ed.) Risk Management: Value at Risk and Beyond. Cambridge Univ. Press, pp 100–128

  • Dempster MAH et al (2006) Managing Guarantees. J. of Portfolio Management, 32, Winter

  • Dentcheva D, Römisch W (2000) Differential stability of two-stage stochastic programs. SIAM J Optimization 11:87–112

    Article  Google Scholar 

  • Dupačová J (1986) Stability in stochastic programming with recourse – contaminated distributions. Math Program Study 27: 133–144

    Google Scholar 

  • Dupačová J (1990) Stability and sensitivity analysis for stochastic programming. Ann Oper Res 27: 115–142

    Article  Google Scholar 

  • Dupačová J (1995) Postoptimality for multistage stochastic linear programs. Ann Oper Res 56: 65–78

    Article  Google Scholar 

  • Dupačová J (1996) Scenario-based stochastic programs: Resistence with respect to sample. Ann Oper Res 64: 21–38

    Article  Google Scholar 

  • Dupačová J (2004) Reflections on output analysis for multistage stochastic linear programs. In: Marti K, Ermoliev Y, Pflug G (eds) Dynamic Stochastic Optimization, LNEMS 532. Springer Verlag, Berlin, pp 3–20

    Google Scholar 

  • Dupačová J (2006a) Contamination for multistage stochastic programs. In: Hušková M, Janžura M (eds.) Prague Stochastics 2006, Matfyzpress, Praha 2006, pp 91–101

  • Dupačová J et al (2006b) Stress testing via contamination. In: Marti K (eds) Coping with Uncertainty. Modeling and Policy Issues, LNEMS 581. Springer Verlag, Berlin, pp 29–46

    Google Scholar 

  • Dupačová J (2008) Risk objectives in two-stage stochastic programming problems. Kybernetika 44: 227–242

    Google Scholar 

  • Dupačová J, Bertocchi M, Moriggia V (1998) Postoptimality for scenario based financial models with an application to bond portfolio management. In: Ziemba WT, Mulvey J (eds.) World Wide Asset and Liability Modeling. Cambridge Univ. Press, pp 263–285

  • Dupačová J, Gröwe-Kuska N, Römisch W (2003) Scenario reduction in stochastic programming: an approach using probability metrics. Math Program A 95: 493–511

    Article  Google Scholar 

  • Dupačová J, Hurt J, Štěpán J (2002) Stochastic Modeling in Economics and Finance. Kluwer Acad. Publ., Dordrecht

    Google Scholar 

  • Dupačová J, Polívka J (2004) Asset-liability management for Czech pension funds using stochastic programming. SPEPS 2004-01, To appear in Ann. Oper. Res

  • Dupačová J, Polívka J (2007) Stress testing for VaR and CVaR. Quantitative Finance 7: 411–425

    Article  Google Scholar 

  • Eichhorn A, Römisch W (2005) Polyhedral risk measures in stochastic programming. SIAM J Optimization 16: 69–95

    Article  Google Scholar 

  • Eichhorn A, Römisch W (2006) Mean-risk optimization models for electricity portfolio management. In: Proc. 9th Int. Conference on Probabilistic Methods Applied to Power Systems (PMAPS 2006), Stockholm

  • Frauendorfer K, Haarbrücker G (2000) Test problems in stochastic multistage programming. Optimization 47: 267–285

    Article  Google Scholar 

  • Frauendorfer K, Marohn Ch (2004) Refinement issues in stochastic multistage linear programming. In: Marti K, Pflug G (eds) Stochastic Programming Methods and Technical Applications, LNEMS 458. Springer Verlag, Berlin, pp 305–328

    Google Scholar 

  • Grinold RC (1986) Infinite horizon stochastic programs. SIAM J Control and Optimization 24: 1246–1260

    Article  Google Scholar 

  • Gol’štejn EG (1972) Theory of Convex Programming. Translations of Mathematical Monographs 36. American Mathematical Society, Providence, RI

  • Gol’štejn EG, Yudin DB (1966) New Directions in Linear Programming [in Russian]. Sovetskoe Radio, Moscow

  • Heitsch H, Römisch W, Strugarek C (2006) Stability of multistage stochastic programs. SIAM J Optimization 17: 511–525

    Article  Google Scholar 

  • Kall P, Mayer J (2005) Stochastic Linear Programming: Models, Theory and Computation. Springer International Series, New York

  • Mulvey JM, Vanderbei RJ, Zenios SA (1995) Robust optimization of large scale systems. Oper Res 43: 264–281

    Article  Google Scholar 

  • Nielsen SS, Poulsen R (2004) A two-factor, stochastic programming model of Danisch mortgage-backed securities. J Econ Dynamics and Control 28: 1267–1289

    Article  Google Scholar 

  • Nielsen SS, Zenios SA (1996) A stochastic programming model for funding single premium deferred annuities. Math Program 75: 177–200

    Google Scholar 

  • Ruszczyński A, Shapiro A (eds.) (2003) Stochastic Programming. Handbooks in Operations Research and Management Science 10, Elsevier, Amsterdam

  • Serfling RJ (1980) Approximation Theorems of Mathematical Statistics. J. Wiley, New York

    Book  Google Scholar 

  • Shapiro A (1990) On differential stability in stochastic programming. Math Program 47: 107–116

    Article  Google Scholar 

  • Shapiro A (2003) Statistical inference of multistage stochastic programming problems. Math Methods of Oper Res 58: 57–68

    Article  Google Scholar 

  • Shapiro A (2008) Stochastic programming approach to optimization under uncertainty. Math Program Ser B 112: 183–220

    Article  Google Scholar 

  • Shapiro JF (1988) Stochastic programming models for dedicated portfolio selection. In: Mitra B (eds) Mathematical Models for Decision Support. NATO ASI Series F48. Springer Verlag, Berlin, pp 587–611

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics Charles University in Prague, Sokolovská 83, 186 75, Praha, Czech Republic

    Jitka Dupačová

  2. Department of Mathematics, Statistic, Computer Science and Applications, Bergamo University, Via dei Caniana 2, Bergamo, 24127, Italy

    Marida Bertocchi & Vittorio Moriggia

Authors
  1. Jitka Dupačová
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marida Bertocchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vittorio Moriggia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jitka Dupačová.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dupačová, J., Bertocchi, M. & Moriggia, V. Testing the structure of multistage stochastic programs. Comput Manag Sci 6, 161–185 (2009). https://doi.org/10.1007/s10287-008-0092-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10287-008-0092-1

Keywords

Search

Navigation