Safety-first portfolio selection

TL;DR: D.A. Roy’s safety-first (SF) approach to financial portfolio optimization is improved by way of a better estimation of the negative return probabilities by means of mean excess return risk functions.

Abstract: A. D. Roy's safety-first (SF) approach to financial portfolio optimization is improved. Safety first means the minimization of the probability of negative returns. The improvement concerns a better estimation of the negative return probabilities by means of mean excess return risk functions. The search for the optimal SF-portfolio is similar to Roy's geometric method but the efficient frontier is different. In case of a finite number of scenarios, the SF-portfolio selection problem is reduced to a mixed linear Boolean programming problem.