Algorithmic Studies on Portfolio Optimization and Asset Pricing and Transaction Cost

我们证明了凹形交易费用下的投资组合优化问题可以用一种新的分支定界算法来求解。长期以来，这类问题在数学优化领域一直被认为是棘手的问题。我们的成功依赖于使用绝对偏差而不是方差作为风险的衡量标准，这使得人们能够应用在线性规划领域开发的许多有效的方案。我们认为，这种方法可以作为处理更困难的哥伦比亚特区的基本工具。与市场影响成本相关的优化问题。我们还表明，对凹形交易成本的精确处理导致了与其线性近似所得到的投资组合显著不同。

We showed that portfolio optimization problems under concave transaction cost can be solved by a newly developed branch and bound algorithm. This class of problems have long been considered to be intractable in the field of mathematical optimization. Our success depends upon the use of absolute deviation instead of variance as a measure of risk, which enables one to apply a number of efficient schemes developed in the field of linear programming. We believe that this method can serve as a basic tool for handling yet more difficult d.c. optimization problems associated with market impact cost.We also showed that an exact treatment of concave transaction cost leads to a significantly different portfolio compared with those obtained by its linear approximation.