MULTI-VALUED OPTIMAL STOPPING PROBLEM WITH MONOTONICITY

We consider a multi-valued optimal stopping problem for indexed random sequences. We perform a scalarization of the random sequences and give characterization of optimal value process for scalarized problem. We also find optimal stopping time in the sense of Pareto optimality for original problem. We apply its result to monotone cases, in which it is given an explicit optimal stopping time. It is given sufficient conditions for our problem to be a monotone case. One of conditions is a kind of concavity with regard to time parameter