Uncertainty and Probability Optimal Stopping

Optimal Stopping Problems: Solution, Discrete Finite

Time

based on R., Econometrica 2009

Solution

Define theSnell envelope Uvia backward induction:

UT=XT

Ut= max{Xt,E[Ut+1|Ft]} (t<T)

Uis the smallest supermartingale≥X

An optimal stopping time is given byτ∗= inf{t≥0 :Xt=Ut}.