We consider dynamic portfolio management problems over a finite horizon and we assume that the uncertainty faced by the investor can be modelled by discrete probability distributions via a scenario approach. To solve the resulting optimization problem we apply a stochastic programming technique based on a scenario decomposition approach. We propose a further decomposition obtained by means of a discrete version of the Maximum Principle thus obtaining a double decomposition of the original problem both with respect to the stochastic aspect and the dynamics over time. Applying this double decomposition to our portfolio problems yields a simpler and more direct solution approach which we illustrate with examples.
Scenario and time decomposition in dynamic portfolio optimization problems
BARRO, Diana;CANESTRELLI, Elio
2004-01-01
Abstract
We consider dynamic portfolio management problems over a finite horizon and we assume that the uncertainty faced by the investor can be modelled by discrete probability distributions via a scenario approach. To solve the resulting optimization problem we apply a stochastic programming technique based on a scenario decomposition approach. We propose a further decomposition obtained by means of a discrete version of the Maximum Principle thus obtaining a double decomposition of the original problem both with respect to the stochastic aspect and the dynamics over time. Applying this double decomposition to our portfolio problems yields a simpler and more direct solution approach which we illustrate with examples.
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