  This paper formed part of a preliminary research report for a risk
consultancy and academic research. Stochastic Programming models provide a
powerful paradigm for decision making under uncertainty. In these models the
uncertainties are represented by a discrete scenario tree and the quality of
the solutions obtained is governed by the quality of the scenarios generated.
We propose a new technique to generate scenarios based on Gaussian Mixture
Hidden Markov Modelling. We show that our approach explicitly captures
important time varying dynamics of stochastic processes (such as autoregression
and jumps) as well as non-Gaussian distribution characteristics (such as
skewness and kurtosis). Our scenario generation method enables richer
robustness and scenario analysis through exploiting the tractable properties of
Markov models and Gaussian mixture distributions. We demonstrate the benefits
of our scenario generation method by conducting numerical experiments on
FTSE-100 data.
