Mean-Absolute Deviation Portfolio Optimization Model Under Transaction Costs

Abstract

We will propese a branch and bound algoriLhm for solving a portfolio optimization model under nonconvex transaction costs, It is well knewn that the llnit transaction cost is larger when the amollnt of

Optimization of a Long-Short Portfolio under Nonconvex Transaction Cost

“…Earlier experiments on concave and d.c. transaction cost problems reported in [10][11][12] show that the amount of computation is highly dependent upon the number of variables. In fact, computation time increases exponentially as n increases.…”

“…Note that the maximal possible amount of fund to be allocated to each individual asset stays in the concave cost region when M is less than 1.0, so that the problem (P 0 ) is essentially a linearly constrained convex maximization problem in this case. As demonstrated in earlier papers [9][10][11], convex maximization problem is much easier than d.c. maximization problem associated with larger amount of fund (M ≥ 1.2).…”

“…We could not obtain any feasible solution after 3000 CPU Time. Therefore we use the branch and bound algorithm which works well for piecewise linear concave function [10], which will be reproduced in the appendix to make the paper self-contained.…”

“…Also, it has a remarkable advantage over variance (standard deviation) since a number of elaborate schemes developed in the field of linear programming can be applied to solve this model. In fact, it has been successfully applied to various optimization problems with nonconvex transaction costs [10][11][12].…”

A sample-path approach to optimal position liquidation

“…For a survey of DC programming algorithms see, for example, Horst and Thoai (1999), Horst, Pardalos, and Thoai (2000), Tuy (1994Tuy ( , 2000, and references therein. Separability of the objective function (20) makes the DC algorithms that exploit this property (e.g., Konno and Wijayanayake (1999)) especially attractive.…”