A global optimization problem in portfolio selection

This paper deals with the issue of buy-in thresholds in portfolio optimization using the Markowitz approach. Optimal values of invested fractions calculated using, for instance, the classical minimum-risk problem can be unsatisfactory in practice because they lead to unrealistically small holdings of certain assets. Hence we may want to impose a discrete restriction on each invested fraction y i such as y i > y min or y i = 0. We shall describe an approach which uses a combination of local and global optimization to determine satisfactory solutions. The approach could also be applied to other discrete conditions—for instance when assets can only be purchased in units of a certain size (roundlots).