Uncertainty and Probability Optimal Stopping Rules

Monotonicity and Stochastic Dominance

Suppose that (Yt) are iid underP∗∈Pand

for allP∈P

P∗[Yt≤x]≥P[Yt≤x] (x∈R)

and suppose that the payoffXt=g(t,Yt) for a functiongthat is

isotone iny,

thenP∗isfor all optimal stopping problems(Xt) theworst–case

measure,

i.e. the robust optimal stopping rule is the optimal stopping rule

underP∗.