Algorithmic Studies on Portfolio Optimization and Asset Pricing and Transaction Cost

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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.