Scenario tree generation through the neural gas algorithm

Abstract

The problem of scenario tree generation is closely related to that of stochastic programming. A natural approach in stochastic programming consists of replacing the continuous random parameters that represent uncertainty by discrete ones that approximate the continuous distribution in some optimal criteria. For multistage stochastic programming, this discrete distribution is usually required to have a tree-shape form, giving a discrete distribution that disclosures with the time realization. The construction of this type of distribution is known as scenario tree generation. Usually, the starting point is a collection of samples obtained from some alternative model or from real data. In this paper it is extended a clustering technique to obtain a family of clusters centers that share the scenario values up to the ramification node. The algorithm is employed to generate multivariate distribution functions that enter into a stochastic portfolio model.