Esscher transforms and the minimal entropy martingale measure for exponential Lévy models

Abstract

In this paper we offer a systematic survey and comparison of the Esscher martingale transform for linear processes, the Esscher martingale trasnform for exponential processes, and the minimal entropy martingale measure for exponential Lévy models and present some new results in order to give a complete characterization of those classes of measures. We illustrate the results with several concrete examples in detail.