2012 Fiscal Year Final Research Report
Study on the nonlinear partial differential equations arising in applied field
| Project/Area Number |
21540117
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Hitotsubashi University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2012
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| Keywords | 非線形偏微分方程式 / 数理モデル / 数理ファイナンス / リスク選好 / コピュラ |
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| Research Abstract |
The study is performed on nonlinear partial differential equations (PDEs) arising in applied field with the purpose of deeply understanding the phenomena represented by the PDEs. We consider the Hamilton-Jacobi-Bellman equation in the optimal investment problem. We derive the slightly general nonlinear PDEs for the risk preference and analyze the equation. Moreover, we study the copula function, which describes the nonlinear relation among random variables. We introduce the time evolution of copulas.Both results are worth advancing the understandings of economics phenomena.
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