Temps D'Arret Optimal, Quasi-Temps D'Arret et Retournement du Temps

Abstract

A generalized problem of optimal stopping is defined, which has a solution in the class of quasi-stopping times, which generalize the classical stopping times. The optimal quasi-stopping times are fully characterized. By time reversal, on a Markov process, various results of Meyer, Mokobodzki and Rost are interpreted as results of existence of optimal quasi-stopping times for the reversed process. Finally, a game on quasi-stopping times is solved.