Robust best choice problem

We consider a robust version of thefull information best choiceproblem: there is model uncertainty, represented by a set of priors, about the measure driving the observed process. We propose a general construction of the set of priors that we use to solve the problem in the setting of Riedel (Econometrica 77(3):857-908, 2009). As in the classical case, it is optimal to stop if the current observation is a running maximum that exceeds certain decreasing thresholds. We characterize the history dependent minimizing measure and perform sensitivity analysis on two examples.