Predicting stock and portfolio returns using mixtures of truncated exponentials

Abstract. This paper presents uses mixtures of truncated exponentials (MTE) potentials in two applications of Bayesian networks to finance problems. First, naive Bayes and TAN models where continuous probability densities are approximated by MTE potentials are used to provide a dis-tribution of stock returns. Second, a Bayesian network is used to determine a return distribution for a portfolio of stocks. Using MTE potentials to approximate the distributions for the continuous variables in the network allows use of the Shenoy-Shafer architecture to obtain a solution for the marginal distributions. We also illustrate the problem that arises in these models where determinis-tic relationships between variables appears, which is related with the partitioning of the domain of the MTE distributions. We propose a solution based on simulation.