Rebalance schedule optimization of a large scale portfolio under transaction cost

This paper is concerned with an optimization problem associated with a rebalancing schedule of a large scale fund subject to nonconvex transaction cost. We will formulate this problem as a 0-1 mixed integer programming problem under linear constraints using absolute deviation as the measure of risk. This problem can be solved by an integer programming software if the size of the universe is small. However, it is still beyond the reach of the state-of-the-art technology to solve a large scale rebalancing problem. We will show that we can now solve these problems almost exactly within a practical amount of time by using an elaborate heuristic approach.