Constrained dynkin's stopping problem with continuous parameter
Yoshio Ohtsubo · Stochastics and stochastics reports · 1989
We consider Dynkin's stopping problem with a finite constraint for right continuous, adapted and bounded processes. In general the minimax value process of the problem does not coincide with the maximin one. We show that there exists a right continuous version of the minimax (maximin) value process, and that the version is the smallest (largest) among right continuous processes satisfying certain stopped martingale inequalities. We then give equivalent conditions for the coincidence of two value processes. The proof of these results is reduced to certain Dynkin's problem without a finite constraint.