Estimation of Optimal Portfolios and Shortfall Probabilities with A Mixture of Gamma Distributions

摘要

We develop a new approach of constructing asymmetric joint probability densities for asset returns by means of the Edgeworth expansions. We also obtain parametric domains on which these densities become valid. We then use the proposed densities to approximate optimal portfolios and the upper bounds of the shortfall probabilities of a portfolio return. Saddlepoint expansions are also derived for the minimum shortfall probability. A Monte Carlo experiment provides strong evidence in favor of using an asymmetric joint distribution for asset returns.