Physical Sciences and Mathematics Commons^™

On Some Optimal Stopping Problems With Constraint, J. L. Menaldi, M. Robin

Mathematics Faculty Research Publications

We consider the optimal stopping problem of a Markov process {x_t : t ≤ 0} when the controller is allowed to stop only at the arrival times of a signal, that is, at a sequence of instants {τ_n : n ≤ 1} independent of {x_t : t ≤ 0}. We solve in detail this problem for general Markov–Feller processes with compact state space when the interarrival times of the signal are independent identically distributed random variables. In addition, we discuss several extensions to other signals and to other cases of state spaces. These results …