跳躍過程及其應用

Abstract

我們探討跳躍隨機過程及其應用。特別的我們研究矩陣型跳 躍擴散過程第一次離開有限區段的泛函問題。我們除了希望得到 此泛函的詳細表示式外也將探討其在邊界的微分表示式。解決上 述這些問題，將有效的協助我們回答一些新奇選擇權的定價及最 佳執行點問題。Given a two-sided matrix exponent jump-diffusion process, we consider a first exit functional of the process from a finite interval. As in our previous works, we will try to derive explicit solutions for the functionals and study its first derivatives on each of its boundaries. These studies will make it possible for exotic option pricing in the general jump process modelling. Also by imposing the smooth pasting assumption, which is always assumed in applied fields such as economics and finance, we can determine the optimal levels for these exotic options. The Novikov-Shiryaev optimal stopping problem is also touched for general Lèvy processes.