Abstract
In the first part of the talk, we characterize the event of convergence of a local supermartingale. Conditions are given in terms of its predictable characteristics and jump measure. Furthermore, it is shown that L^1-boundedness of a related process is necessary and sufficient for convergence. The notion of extended local integrability plays a key role. In the second part of the talk, we provide a novel proof for the sufficiency of Novikov-Kazamaki type conditions for the martingale property of nonnegative local martingales with jumps. The proof is based on explosion criteria for related processes under a possibly non-equivalent measure.
This is joint work with Martin Larsson.