On the predictable representation property of martingales associated with Lévy processes

Abstract

We investigate the predictable representation property (PRP) in the frame of Lévy processes. To give a general definition of the PRP, we make use of the theory of stable subspaces. Let L be a Lévy process with Lévy measure . The main result is that any total system in leads to a family of martingales with the PRP.

Keywords::

• Lévy processes
• stable subspaces
• Poisson random measure
• predictable representation property
• Teugels martingales

MSC (2010) Classification::

• Primary 60H05
• 60G44
• 60G51
• Secondary 60G57
• 60G52

Acknowledgement

This work has been financially supported by the European Community's FP 7 Program under contract PITN-GA-2008-213841, Marie Curie ITN ‘Controlled Systems’.