## Section: New Results

### Optimal stopping and American Options

Participants : D. Lamberton, M. Mikou, M.C. Quenez.

- D. Lamberton is working on optimal stopping of one-dimensional diffusions with Mihail Zervos (previously at King's College, London, now at the London School of Economics). They have submitted a paper on the infinite horizon case and are currently working on the finite horizon case.

- D. Lamberton and his 1st year PhD student Mohammed Mikou are studying American options in exponential Lévy models. They have studied some properties of the exercise boundary of the American put option in an exponential Lévy model (continuity of the exercise boundary, behavior near maturity).

M.C. Quenez, Magdalena Kobylanski and Elizabeth Rouy have studied the multitiple stopping time problem where is the set of stopping times and :(t, s, )(t, s, ) is -adapted. They have shown that under some smoothness assumptions on (right-continuity w.r.t. t (resp. s) uniformly w.r.t s (resp. t), the value function can be characterized as the Snell enveloppe associated with a progressive reward process which can be completely determined.