TY - JOUR
T1 - A primal-dual decomposition-based interior point approach to two-stage stochastic linear programming
AU - Berkelaar, Arjan
AU - Dert, Cees
AU - Oldenkamp, Bart
AU - Zhang, Shuzhong
PY - 2002
Y1 - 2002
N2 - 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.
AB - 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.
KW - Programming
KW - Stochastic: decomposition and interior point methods
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U2 - 10.1287/opre.50.5.904.360
DO - 10.1287/opre.50.5.904.360
M3 - Article
AN - SCOPUS:0036759227
VL - 50
SP - 904
EP - 915
JO - Operations Research
JF - Operations Research
SN - 0030-364X
IS - 5
ER -