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On filtration enlargements and purely discontinuous martingales
 

Summary: On filtration enlargements and purely discontinuous
martingales
Stefan Ankirchner
Institut f¨ur Mathematik
Humboldt-Universit¨at zu Berlin
Unter den Linden 6
10099 Berlin
Germany
November 7, 2007
Abstract
Let M be a purely discontinuous martingale relative to a filtration
(Ft). Given an arbitrary extension (Gt) of the filtration (Ft), we will
provide sufficient conditions for M to be a semimartingale relative to
(Gt). 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.
2000 AMS subject classifications: primary 60H07, 60G44; sec-
ondary 60G57.

  

Source: Ankirchner, Stefan - Institut für Angewandte Mathematik, Universität Bonn

 

Collections: Mathematics