On filtration enlargements and purely discontinuous martingales

Stefan Ankirchner

Stochastic Processes and their Applications, 2008, vol. 118, issue 9, 1662-1678

Abstract: Let M be a purely discontinuous martingale relative to a filtration . Given an arbitrary extension of the filtration , we will provide sufficient conditions for M to be a semimartingale relative to . Moreover we describe methods of how to find the Doob-Meyer decomposition with respect to the enlarged filtration. To this end we prove a new and more explicit version of the predictable representation property of Poisson random measures. Finally some concrete examples will show how the method developed may be applied.

Keywords: Enlargement; of; filtrations; Semimartingale; Doob-Meyer; decomposition; Purely; discontinuous; martingale; Poisson; random; measure; Predictable; representation; Picard's; difference; operator (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (4)

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