Integer programming approaches in mean-risk models

This paper is concerned with portfolio optimization problems with integer constraints. Such problems include, among others, mean-risk problems with nonconvex transaction cost, minimal transaction unit constraints and cardinality constraints on the number of assets in a portfolio. These problems, though practically very important, have been considered intractable because we have to solve nonlinear integer programming problems for which there exist no efficient algorithms. We will show that these problems can now be solved by the state-of-the-art integer programming methodologies if we use absolute deviation as the measure of risk.