Mathematics for Economists

Optimal stopping

DeÖnition

LetHt0 be a set of random payouts. The optimal stopping problem is

to Önd

sup

τ

E(H(τ))

whereτis an arbitrary stopping time. (A discrete random variableτis a

stopping time iffτ=tg2 Ftfor everytwhereFtis the set of

observable events at timet. This means that at every moment of timet

the condition of stopping is known at that moment. We want to exclude

referring for the future in the conditions of stopping.)