A Parametric Linear Complementarity Technique for Optimal Portfolio Selection with a Risk-Free Asset

Abstract

The general single-period optimal portfolio selection problem with a risk-free asset can be solved by a two-stage approach. In the first stage, one solves a certain fractional program, and in the second, a simple stochastic program with one single variable. This paper proposes a parametric approach for the solution of the fractional program via its equivalent linear complementarity formulation. In the latter part of the paper, we specialize the proposed method to a specific model of the portfolio problem with upper bounds and outline how the method can take advantage of the special structure arising from the model. Finally, we report some computational results and a brief comparison between our method and Lemke's algorithm.