Portfolio selection: A linear approach with dual expected utility

This paper analyses the portfolio selection problem under the non-expected utility theory. We assume that the decision maker ranks the alternatives by using a specific dual expected utility. This function allows returns which are less than or equal to a fixed benchmark to be weighted in a different way from those greater than the fixed benchmark. In this model the implicit risk measure is more general than the standard deviation and it coincides with the downside risk only due to the appropriate choices of the parameters. Under normally distributed returns and appropriate choices of the benchmark, the approach suggested is equivalent to the Markowitz model in term of efficient frontier and moreover has the advantage of using linear programming to obtain the optimal portfolio. It can thus handle high dimensional problems. We also show results obtained by implementing the model on the Italian stock market.