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

点击翻译按钮获取中文摘要

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.