| Project/Area Number |
17K05297
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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 |
Basic analysis
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| Research Institution | Osaka 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 |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 後退確率微分方程式 / 非線形確率積分 / 確率解析 / 数理ファイナンス / 確率論 / 解析学 |
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| Outline of Final Research Achievements |
We studied backward stochastic differential equation and nonlinear stochastic integration with applications to mathematical finance. This project was motivated by an idea to model Profit and Loss under a nonlinear market, where the nonlinearity is due to permanent market impacts, by a nonlinear stochastic integral, and that the nonlinear stochastic integral can be linearized in a sense by using a solution of a backward stochastic differential equation. By assuming a Bertrand-type competition with utility function modeled by a nonlinear conditional expectation, we derive a perfect hedging strategy under this market. Under the simplest setting the hedging strategy is a solution of Burgers' equation, and we find a mechanism that an endowment shock is propagated along Burgers' equation to invoke a crash in the underlying asset price.
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| Academic Significance and Societal Importance of the Research Achievements |
後退確率微分方程式と非線形確率微分方程式の関係が明らかとなり、伊藤の表現定理の非線形確率積分への拡張や、後退確率微分方程式の解の非退化性など確率解析分野における新しい知見が得られた。これら数学的成果の帰結として、ファイナンスモデルの解析により市場の非線形性に関する斬新な解釈とリスクヘッジ手法が得られ、流動性リスクの考慮を通した金融工学技術の発展を通して、金融市場の安定化に貢献する。
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