The pricing measure for geometric Levy processes under incomplete financial markets

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. Key words: minimal entropy martingale measure, exponential Levy process, stochastic exponential of Levy process