INTRODUCTION TO KUSUOKA APPROXIMATIONS

摘要

In order to represent varying time changing phenomena, dynamic systems are often used in various fields. Specifically in financial engineering, one frequently uses noise driven models. From these random dynamical systems, several random variables of interest are generated. An important goal is to calculate the expectation of functionals with respect to these generated random variables. One of the most used noise process in these dynamical systems is the Brownian motion process. But, as in many other models, financial markets exhibit jumps and therefore some jump type noise processes are adopted, for example, the Variance Gamma model, the Hyperbolic model, the Inverse Gaussian model and so on. One of the characteristics of these models is that the driving process has infinitely many jumps in any compact interval.