* This research is supported by CARF (Center for Advanced Research in Finance) and the global COE program "The research and training center for new development in mathematics." We are very grateful to two anonymous referees for their precious comments, which have improved the previous version of this paper substantially. Also, we thank Hideki Yamauchi and Takahiko Suenaga at GCI Asset Management Inc. and Tetsuya Aoki at GCI Investment Management Singapore Pte. Ltd. for their constant support. All the contents expressed in this research are solely those of the authors and do not represent any views or opinions of any institutions. The authors are not responsible or liable in any manner for any losses and/or damages caused by the use of any contents in this research. Takahashi and Yamamoto (2010) is the summary of this research. It is based on the presentation entitled "A New Hedge Fund Replication Method with the dynamic Optimal Portfolio at Global Conference on Business and Finance 2010