Optimal portfolios with Haezendonck risk measures

Abstract

We deal with the problem of the practical use of Haezendonck risk measures (see Haezendonck and Goovaerts [8], Goovaerts et al. [7], Bellini and Rosazza Gianin [4]) in portfolio optimization. We first analyze the properties of the natural estimators of Haezendonck risk measures by means of numerical simulations and point out a connection with the theory of M-functionals (see Hampel [9], Huber [11], Serfling [19]) that enables us to derive analytic results on the asymptotic distribution of Orlicz premia. We then prove that as in the CVaR case (see Rockafellar and Uryasev [17,18], Bertsimas et al. [6]) the mean/Haezendonck optimal portfolios can be obtained through the solution of a single minimization, and that the resulting efficient frontiers are convex. We conclude with a real data example in which we compare optimal portfolios generated by a mean/Haezendonck criterion with mean/variance and mean/CVaR optimal portfolios.