Approaching mixed-integer nonlinear mean-variance portfolio selection

(Pubblicazione citata nel repertorio MathSciNet, riferimento n. MR1701159; pubblicazione citata nel repertorio Zentralblatt MATH, riferimento n. Zbl 0976.91035)

Generally, in the classical mean-variance portfolio selection approach, several realistic features are not taken into acount. Among these "forgotten" aspects, one of particular interest is the not finite divisibility of the financial asset to select, i.e. the obligation to buy/sell only integer quantities of asset lots whose numerousness is predetermined. In order to consider such a feature, we deal with a suitably defined mixed-integer nonlinear programming problem. In particular, first we propose a formulation of this problem in terms of quantities, i.e. integer numbers of asset lots to buy/sell, instead of starting capital percentages; second, we give necessary and sufficient conditions for the existence of feasible solution(s); third, we propose an algorithm for finding a "good" feasible solution and prove its convergence; finally, we give some numerical examples illustrating the previous points.