Complex System Based Mathematical Analysis of Non-normal Distribution Family and Stochastic Differential Equation and Their Applications to Risk Management

基于复杂系统的非正态分布族和随机微分方程的数学分析及其在风险管理中的应用

• 批准号: 19510164
• 负责人: TAN Kangrong
• 金额: $ 2.91万
• 依托单位: Kurume University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19510164/
• 关键词: 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; 非正規分布; 確率微分法方程式

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.

本文研究了非正态分布族(在某些情况下扩散了一个非线性时间因素)和基于非布朗运动的随机微分方程(SDE)的数学性质及其应用。主要研究和发展了以下理论或应用。1)基于混合分布族或非正态分布族的随机过程识别；2)基于混合分布族的尾部分布分析和非正态现象下的重要抽样方法，如重尾分布；3)SDE行为的理论和数值分析，例如具有跳跃因子的SDE。在我们的研究中，统计方法和基于复杂系统的遗传方法被应用于参数优化。

项目成果

THE EXISTENCE AND UNIQUENESS FOR NON-LIPSCHITZ STOCHASTIC NEUTRAL DELAY EVOLUTION EQUATIONS DRIVEN BY POISSON JUMPS

• DOI: 10.1142/s0219493709002592
• 发表时间: 2009-03
• 期刊: Stochastics and Dynamics
• 影响因子: 1.1
• 作者: Jiaowan Luo;T. Taniguchi

Estimation of Portfolio Return and the Value at Risk based upon a Class of Gaussian Mixture Distributions

基于一类高斯混合分布的投资组合收益和风险价值的估计

• 发表时间: 2011
• 期刊: Proc.of Global Conference on Business and Finance 2011
• 作者: Kangrong Tan;Meifen Chu
• 通讯作者: Meifen Chu

遺伝的プログラミングによる方程式近似に基づく粒子フィルタを用いた時系列からの状態推定とその変動抑制への応用

基于遗传规划方程近似的粒子滤波器时间序列状态估计及其在波动抑制中的应用

• 发表时间: 2010
• 期刊: 電子情報学会論文誌(A) J93-A(11)
• 作者: 時永祥三;譚康融
• 通讯作者: 譚康融

The existence and uniqueness for non-Lipschitz stochastic neutral equations driven by poisson jumps

泊松跳跃驱动的非Lipschitz随机中性方程的存在唯一性

• 发表时间: 2009
• 期刊: Journal of Stochastics and Dynamics 9 (2)
• 作者: Jiaowan Luo;Takeshi Taniguchi
• 通讯作者: Takeshi Taniguchi

On the mode of a Convo-lution Density of the Scaled Normal and Pearson Type VII Distributions

关于标度正态分布和皮尔逊VII型分布的卷积密度模

• 发表时间: 2011
• 期刊: Theoretical Advances and Applications in Operations Research
• 作者: 仲谷美江;他;譚康融
• 通讯作者: 譚康融