2010 Fiscal Year Final Research Report
Complex System Based Mathematical Analysis of Non-normal Distribution Family and Stochastic Differential Equation and Their Applications to Risk Management
| Project/Area Number |
19510164
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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 |
Social systems engineering/Safety system
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| Research Institution | Kurume University |
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Principal Investigator |
TAN Kangrong Kurume University, 経済学部, 教授 (70368968)
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| Co-Investigator(Kenkyū-buntansha) |
HARADA Kouhei 久留米大学, 経済学部, 教授 (30091359)
TANIGUCHI Takeshi 久留米大学, 文学部, 教授 (00102096)
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| Project Period (FY) |
2007 – 2010
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| Keywords | モデリング / リスク管理 / 確率微分方程式 / 複雑系 / 非正規分布族 |
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| Research Abstract |
This research aims to study the mathematical properties of non-normal distribution family, in some cases which is diffused with a nonlinear time factor, and the non-Brownian motion based Stochastic Differential Equation (SDE), and their applications. Mainly, the following theories or applications have been studied and developed. 1)Identification of a stochastic process based upon mixture distribution family, or non-normal distribution family ; 2)Analysis of tail distribution based upon mixture distribution family and the Importance Sampling Method under the non-normal phenomena, such as, heavy-tail distributions ; 3)Analysis of behavior of SDEs theoretically and numerically, such as a SDE having a jump factor. In our studies, statistical methods and complex system based genetic methods have been applied to parameter optimization.
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