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 |
Section | 一般 |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
Research Institution | Hitotsubashi University |
Principal Investigator |
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Project Period (FY) |
2009 – 2012
|
Project Status |
Completed (Fiscal Year 2012)
|
Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
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 / 拡散方程式 / 定量的リスク管理 / 離散化 / HJB方程式 / 進行波解 / 数値計算 / Hamilton-Jacobi-Bellman方程式 / リスク相関 / 時間発展 / 最適化問題 / 確率制御 / 数値解法 |
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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Report
(5 results)
Research Products
(28 results)