Mathematics for Economists

Optimal stopping

If(ξn)are uniform on[ 0. 1 ]then

αT = 0 ,

αn =

1

1 +r

α^2 n+ 1 +



x^2

2

 1

αn+ 1

!

=

1

1 +r



α^2 n+ 1 +

1

2

α^2 n+ 1

2



=

=

1

2 ( 1 +r)

α^2 n+ 1 + 1

.

IfT=3 andr= 100 %then

α 3 = 0 ,α 2 =

1

4 ,α^1 =

1

4



1

16 +^1



=

17

64.