Multi-period stochastic portfolio optimization: Block-separable decomposition

We consider a multiperiod stochastic programming recourse model for stock portfolio optimization. The presence of various risk and policy constraints leads to significant period-by-period linkage in the model. Furthermore, the dimensionality of the model is large due to many securities under consideration. We propose exploiting block separable recourse structure as well as methods of inducing such structure within nested L-shaped decomposition. We test the model and solution methodology with a base consisting of the Standard & Poor 100 stocks and experiment with several variants of the block separable technique. These are then compared to the standard nested period-by-period decomposition algorithm. It turns out that for financial optimization models of the kind that are discussed in this paper, significant computational efficiencies can be gained with the proposed methodology.