Before revision: The theory of L\'evy models for asset pricing simplifies considerably if one takes a pricing kernel approach, which enables one to bypass market incompleteness issues. The special case of a geometric L\'evy model (GLM) with constant parameters can be regarded as a natural generalisation of the standard geometric Brownian motion model  used in the  Black-Scholes theory .
After revision: The geometric L\'evy model (GLM) with constant parameters can be regarded as a natural generalisation of the standard geometric Brownian motion model used in the Black-Scholes theory .