Temps d'arrêt algébriquement prévisibles
Temps d'arrêt optimaux et théorie générale
Temps d'arrêt riches et applications
Temps d'arrêt totalement inaccessibles
The Banach space of workable contingent claims in arbitrage theory
The measurability of hitting times.
The representation of Poisson functionals
The secretary problem : optimal selection with batch-interviewing and cost
The Skorokhod embedding problem and its offspring.
The Stopping Distributions of a Markov Process.
The "Thirty-seven Percent Rule" and the secretary problem with relative ranks
We revisit the problem of selecting an item from n choices that appear before us in random sequential order so as to minimize the expected rank of the item selected. In particular, we examine the stopping rule where we reject the first k items and then select the first subsequent item that ranks lower than the l-th lowest-ranked item among the first k. We prove that the optimal rule has k ~ n/e, as in the classical secretary problem where our sole objective is to select the item of lowest rank;...
Théorème de séparation dans le problème d'arrêt optimal
Théorie générale et changement de temps
Time-homogeneous diffusions with a given marginal at a random time
We solve explicitly the following problem: for a given probability measure μ, we specify a generalised martingale diffusion (Xt) which, stopped at an independent exponential time T, is distributed according to μ. The process (Xt) is specified via its speed measure m. We present two heuristic arguments and three proofs. First we show how the result can be derived from the solution of [Bertoin and Le Jan, Ann. Probab. 20 (1992) 538–548.] to the Skorokhod embedding problem. Secondly, we give a proof...
Time-homogeneous diffusions with a given marginal at a random time
We solve explicitly the following problem: for a given probability measure μ, we specify a generalised martingale diffusion (Xt) which, stopped at an independent exponential time T, is distributed according to μ. The process (Xt) is specified via its speed measure m. We present two heuristic arguments and three proofs. First we show how the result can be derived from the solution of [Bertoin and Le Jan, Ann. Probab.20 (1992) 538–548.] to the Skorokhod embedding problem. Secondly, we give...
Topics in Markov Additive Processes.
Transitivity and approximate transitivity in problems of optimal stopping
Two-sided exit problem for a spectrally negative -stable Ornstein-Uhlenbeck process and the Wright's generalized hypergeometric functions.