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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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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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 / ポートフォリオ / レプリカ法 / ポートフォリオ最適化問題 / 平均分散モデル / 現在価値 / ランダム行列 / ピタゴラス定理 / 主双対定理 / 自己平均性 / OR / 数理ファイナンス |
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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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| 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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Report
(5 results)
Research Products
(9 results)
