The Pricing Measure for Geometric Levy Ptocesses under Incomplete Financial Markets

本文以Esscher測度轉換建構幾何李維過程的平賭測度，並籍也指數李維過程與李維過程之隨機指數的關係，證明李維過程仍是平賭過程之若且唯若條件，為李維過程的隨機指數亦是平賭過程。根據此一結果，我們得到Esscher測度為最小熵平時測度的必要條件。In this paper, Esscher transformation is applied to construct a martingale measure in the framework of geometric Levy process. By means of a relation between exponential Levy process and stochastic exponential of Levy process, it is shown that a Levy process is a martingale if and only if its stochastic exponential is a martingale. While Esche and Schweizer(2005) offer the sufficient condition for the Esscher measure to be the minimal entropy martingale measure, we provide the necessary condition for the statement to be true based on the above result.