Tomás Prieto Rumeau

Statistical Inference for a Finite Optimal Stopping Problem with Unknown Transition Probabilities

In this paper we consider a finite optimal stopping problem with unknown stationary transition probabilities. The payoffs are assumed to be known. We estimate the value of stationary deterministic decision rules, and then we obtain estimators of an optimal decision rule and the optimal value of the problem that are consistent with probability one. Two different methods are studied: the maximum likelihood estimator and a new procedure, that we will call the stretch estimator, which turns out to be a more efficient technique.