矩陣指數跳躍下Levy過程通過時間之研究

Abstract

考慮一個 Lêvy 過程，其跳躍分佈是矩陣指數型分佈。我們用 Feynman-kac 邊界值問題來處理關於此過程第一次離開任何開集合的泛函 問題。我們用ODE 方法來解此邊界值問題並且研究其在財務方面的應用。Consider a jump diffusion process whose drift function and volatility function is state-dependent and jumps are determined by a state-independent two-sided matrix exponential distribution. We propose the Feynman-Kac boundary value problem for a general first exit function of the process from an open set. We will tackle this boundary value problem via an ODE method. Many interesting financial applications of our approach are expected and our work will generalize those in Asmussen et al.(2004), Chen et al.(2007) and many others.