- Date: 10 Dec. (Thu.)
- Place: On the Web
- Time: 16:30 – 18:00
- Speaker: Anna Aksamit (University of Sydney)
- Title: Progressive enlargements of filtration: overview, new types, and applications
- Abstract:
I will start with reviewing the classical results about enlargement of filtration. The main challenge is to find conditions under which martingales in the reference filtration remain semimartingales in the large filtration. If this is the case, the canonical decomposition is of particular interest. I will then present enlargement of a reference filtration through the observation of a random time and a mark. Random time considered is such that its graph is included in the countable union of graphs of stopping times. Mark revealed at this random time is assumed to satisfied generalised Jacod’s condition. Classical Jacod’s condition concerns initial enlargements and says that the conditional law of a random variable w.r.t. elements of a reference filtration is absolutely continuous w.r.t. its unconditional law. Our relaxation of Jacod’s condition accounts for the dynamic structure of the problem. Finally, I will mention some applications of progressive enlargements, in particular to optimal stopping problem.
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