A Primal-Dual Decomposition-Based Interior Point Approach to Two-Stage Stochastic Linear Programming

Arjan Berkelaar (), Cees Dert (), Bart Oldenkamp () and Shuzhong Zhang ()
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Arjan Berkelaar: Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands
Cees Dert: ABN-AMRO Asset Management, and Faculty of Economic Sciences and Econometrics, Free University of Amsterdam, The Netherlands
Bart Oldenkamp: ABN-AMRO Asset Management, and Econometric Institute, Erasmus University Rotterdam, The Netherlands
Shuzhong Zhang: Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong

Operations Research, 2002, vol. 50, issue 5, 904-915

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 which 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 decomposition 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 with our model with market prices of options on the S&P500.

Keywords: Programming; stochastic: decomposition and interior point methods (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (7)

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