仿射過程及其應用

Abstract

仿射過程是種取值於m個正實數值及n個實數值的馬可夫過程，而仿射過程的特殊性質能廣泛的處理財務上的問題。Duffie、 Filipovic、 Schachermeyer完整刻劃出仿射過程的主要特徵，再者仿射過程和超擴散過程的關係也已被建立。基於這些觀察我們能建構更多仿射過程來處理財務上的問題。

Affine processes is a class of Markov processes taking values in Rm+ × Rn. The rich variety of alternative types of random behavior (e.g., mean reversion,stochasticvolatility, and jumps) and analytically tractable for affine processes make them ideal models for financial applications. Duffie, Filipovic and Schachermayer[DFS03]characterized all regular affine processes. Connections between regular affine processes and superprocesses with a finite base space were also established. Based on this observation, we construct more general affine processes and investigate sample path properties and financial applications of these processes.