BSDEs and log-utility maximization for Lévy processes

Abstract

In this paper we establish the existence and the uniqueness of the solution of a special class of BSDEs for Lévy processes in the case of a Lipschitz generator of sublinear growth. We then study a related problem of logarithmic utility maximization of the terminal wealth in the filtration generated by an arbitrary Lévy process.

Keywords

• Lévy processes
• predictable representation property
• BSDEs
• utility maximization