| Project/Area Number |
15K20999
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Money/ Finance
Social systems engineering/Safety system
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| Research Institution | Hitotsubashi University |
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Principal Investigator |
SHINZATO TAKASHI 一橋大学, 森有礼高等教育国際流動化センター, 講師 (70574614)
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| Project Period (FY) |
2015-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | ポートフォリオ最適化 / 情報統計力学 / レプリカ解析 / 確率伝搬法 / ランダム行列 / 自己平均性 |
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| Outline of Final Research Achievements |
We have examined the optimal solutions of ones of the most fundamental models in portfolio optimization problem using replica analysis and random matrix theory. Especially, it is known that the optimal portfolio which can minimize the investment risk is hard to assess using the previous approach based on operations research and its optimal portfolio is not consistent with the portfolio which can minimize the expected investment risk. In this work, we have examined that the typical behaviors of the minimal investment risk per asset and its investment concentration of the optimal portfolio are easy to resolve using replica analysis. Moreover, from our findings, the Pythagorean theorem of Sharpe ratio was derived easily, and it implies a novel frontier in mathematical finance.
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