Mixed-integer non-linear programming methods for mean-variance portfolio selection

(Journal cited in: MathSciNet, n. MR1940218)In standard mean-variance portfolio selection, several simplifying hypotheses are usually assumed. On the contrary, in this paper we weaken some of the most common of them and propose a problem of portfolio selection in which the following realistic aspects are taken into account: the impossibility of short sale of the assets; their not infinite divisibility; and the presence of transaction costs and taxation. The mathematical formulation of this selection problem is given in terms of mixed-integer non-linear programming one. In order to find its optimal solution (if any) we developed a two-stage solving algorithm (which is bases on the branch and bound methods, the cutting plane one and the sub-gradient method), and prove its convergence in a finite number of iterations