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 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.
|Keywords||decomposition methods, large scale problems, optimization techniques, portfolio choice, stochastic programming|
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 (No. EI 9918-/A). Retrieved from http://hdl.handle.net/1765/1588