Convergence of local supermartingales and Novikov-Kazamaki type conditions for processes with jumps

Martin Larsson; Johannes Ruf

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arXiv · 1411.6229

Convergence of local supermartingales and Novikov-Kazamaki type conditions for processes with jumps

Martin Larsson·Johannes Ruf

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Abstract

We characterize the event of convergence of a local supermartingale. Conditions are given in terms of its predictable characteristics and quadratic variation. The notion of extended local integrability plays a key role. We then apply these characterizations to provide a novel proof for the sufficiency and necessity of Novikov-Kazamaki type conditions for the martingale property of nonnegative local martingales with jumps.

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Martin Larsson, Johannes Ruf. 2014-11-23. Convergence of local supermartingales and Novikov-Kazamaki type conditions for processes with jumps. https://arxiv.org/abs/1411.6229

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