2020 Fiscal Year Final Research Report
Statistical Mechanical Informatics for Priaml-Dual Structure and Macroscopic Theory Included in Portfolio Optimization Problem
| Project/Area Number |
17K01249
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Social systems engineering/Safety system
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| Research Institution | Tamagawa University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Keywords | 情報統計力学 / ポートフォリオ最適化 / 金融工学 / レプリカ解析 / 確率伝搬法 |
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| Outline of Final Research Achievements |
In recent years, research has been conducted to elucidate portfolio optimization problems using statistical mechanical informatics that can overcome these difficulties, except but for portfolio optimization problems with multiple constraints. Not enough research has discussed the primal-dual structure, the mathematical structure of each optimal solution, and the relational expression between macro variables. Therefore, through this research, we compare the investment risk minimization problem (primal problem) and the expected return maximization problem (dual problem) using statistical mechanical informatics, and disclose their primal-dual structure and macroscopic theory.
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| Free Research Field |
情報統計力学
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| Academic Significance and Societal Importance of the Research Achievements |
ポートフォリオ最適化問題に対する情報統計力学の研究はこれまでにもいくつ か行われているが，投資システムを主双対構造の観点から正しく議論することにより，そこで得られた成果は実際の投資行動の最適な指針になる (投資家の期待に応える知見を提供できる ) と 予想される．さらに本研究により，情報統計力学を通してポートフォリオ最適化問題を他分野と関連付けることで，有機的で学際領域的な研究分野に発展することができた．
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