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

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 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 our model with market prices of options on the S&P500. AMS Classification: 49M27 (Decomposition Methods), 90C06 (Large-Scale Problems), 90C15 (Stochastic Programming). JEL Classification: C61 (Optimization Techniques), G11 (Portfolio Choice) ∗Econometric Institute, Erasmus University Rotterdam, P.O.Box 1738, 3000 DR Rotterdam, The Netherlands, [email protected]. †ABN-AMRO Asset Management; Faculty of Economic Sciences and Econometrics, Free University of Amsterdam, The Netherlands, [email protected]. ‡ABN-AMRO Asset Management; Econometric Institute, Erasmus University Rotterdam, The Netherlands, [email protected]. §Corresponding Author. Department of Systems Engineering & Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong, [email protected].