Apr 2014-Mar 2015

Math-Fi seminar on 26 Feb.

2015.02.22 Sun up
  • Date : 26 Feb. (Thu)
  • Place: W.W. 7th-floor, 4th lab.
  • Time : 17:00 – 18:00
  • Speaker: Claude Martini (Zeliade Systems)
  • Title: “Martingale measures with pre-specified marginals: extremal points and perturbations” (joint work with L. Campi, London School of Economics)
  • Abstract: The extremal points in the set of all measures with pre-specified marginals, ***without the martingale constraint***, have been extensively studied by many authors ​in the past (e.g. Denny, Douglas, Letac, Klopotowski to cite only a few).

In this talk, we will focus on the characterization provided by Denny in the countable case: a key property is that the support of the probability Q has no “cycle”, otherwise a perturbation of Q can be constructed so that Q can not be extremal.

In the context of the 2 marginals martingale problem studied by Beiglböck-Juillet, with special cases provided by Henry-Labordère and Touzi, Hobson and Klimmeck, Hobson and Neuberger, and Laachir, we give an analogous “cycle-like” property that corresponds to martingale perturbations.

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