Mathematics for Economists

Optimal stopping

αT = E(ξT)

αn = αn+ 1 ( 1 F(αn+ 1 ))+

Zαn+ 1

0

xdF(x)

If(ξn)is uniform on[ 0 , 1 ], then

αT =

1

2

αn = αn+ 1 ( 1 αn+ 1 )+

α^2 n+ 1

2

=αn+ 1 

α^2 n+ 1

2

.