Portfolio Selection Under Buy-In Threshold Constraints Using DC Programming and DCA

Abstract

In matter of Portfolio selection, we consider a generalization of the Markowitz Mean-Variance model which includes buy-in threshold constraints. These constraints limit the amount of capital to be invested in each asset and prevent very small investments in any asset. The new model can be converted into a NP-hard mixed integer quadratic programming problem. The purpose of this paper is to investigate a continuous approach based on DC programming and DCA for solving this new model. DCA is a local continuous approach to solve a wide variety of nonconvex programs for which it provided quite often a global solution and proved to be more robust and efficient than standard methods. Preliminary comparative results of DCA and a classical Branch-and-Bound algorithm will be presented. These results show that DCA is an efficient and promising approach for the considered portfolio selection problem.

Proceedings of third International Conference on Service Systems and Service Management (SSSM'06/IEEE), Troyes, Oct. 2006, pp. 296-300 (2006). arXiv admin note: text overlap with arXiv:cs/0501005 by other authors