Optimisation of Stochastic Programming by Hidden Markov Modelling based Scenario Generation

Abstract

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.