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A primal-dual decomposition based interior point approach to two-stage stochastic linear programming

Author

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  • Berkelaar, A.B.
  • Dert, C.L.
  • Oldenkamp, K.P.B.
  • Zhang, S.

Abstract

Decision making under uncertainty is a challenge faced by many decision makers. Stochastic programming is a major tool developed to deal with optimization with uncertainties that has found applications in, e.g. finance, such as asset-liability and bond-portfolio management. Computationally however, many models in stochastic programming remain unsolvable because of overwhelming dimensionality. For a model to be well solvable, its special structure must be explored. Most of the solution methods are based on decomposing the data. In this paper we propose a new decomposition approach for two-stage stochastic programming, based on a direct application of the path-following method combined with the homogeneous self-dual technique. Numerical experiments show that our decomposition algorithm is very efficient for solving stochastic programs. In particular, we apply our deompostition method to a two-period portfolio selection problem using options on a stock index. In this model the investor can invest in a money-market account, a stock index, and European options on this index with different maturities. We experiment our model with market prices of options on the S&P500.

Suggested Citation

  • Berkelaar, A.B. & Dert, C.L. & Oldenkamp, K.P.B. & Zhang, S., 1999. "A primal-dual decomposition based interior point approach to two-stage stochastic linear programming," Econometric Institute Research Papers EI 9918-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1588
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    References listed on IDEAS

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    1. Luo, Z-Q. & Sturm, J.F. & Zhang, S., 1996. "Duality and Self-Duality for Conic Convex Programming," Econometric Institute Research Papers EI 9620-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Stein W. Wallace & Stein-Erik Fleten, 2002. "Stochastic programming in energy," GE, Growth, Math methods 0201001, University Library of Munich, Germany, revised 13 Nov 2003.
    3. Yinyu Ye & Michael J. Todd & Shinji Mizuno, 1994. "An O(√nL)-Iteration Homogeneous and Self-Dual Linear Programming Algorithm," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 53-67, February.
    4. John R. Birge & Liqun Qi, 1988. "Computing Block-Angular Karmarkar Projections with Applications to Stochastic Programming," Management Science, INFORMS, vol. 34(12), pages 1472-1479, December.
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    Cited by:

    1. Zhang, S., 2002. "An interior-point and decomposition approach to multiple stage stochastic programming," Econometric Institute Research Papers EI 2002-35, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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    More about this item

    Keywords

    decomposition methods; large scale problems; optimization techniques; portfolio choice; stochastic programming;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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