Mathematics for Economists

Optimal stopping

In our case as the o§ers are independent so

E(Xt+ 1 j Ft)=E(Xt+ 1 )

and the Snell envelope is

Xt = max(Ht,E(Xt+ 1 ))=max



ξt( 1 +r)Tt,E(Xt+ 1 )



=

= max

ξt( 1 +r)Tt,(^1 +r)

TtE(Xt+ 1 )

( 1 +r)Tt

!

$

$ ( 1 +r)Ttmax(ξt,αt)

αT$ 0 ,αt$ E(Xt+^1 )

( 1 +r)Tt

.