Mathematics for Economists

Optimal stopping

Letr=0 and letξuniformly distributed on[ 0 , (^1) ]and letT= 3.

1. If you are in periodt=T= 3 ,you have no choice, so your expected
   payout isE(ξ 3 )= 1 / 2.


2. If you are in periodt=T 1 = 2 ,then you should not take the
   variable ifξ 2 <E(ξ 3 )= 1 /2 because if you wait one period more your
   expected payout is 1/ 2 ,which is better. Your expected payout is

E



max



1

2 ,ξ^2



=

Z 1 / 2

0

1

2 dx+

Z 1

1 / 2

xdx=

=

1

4 +



x^2

2

 1

1 / 2

=

1

4 +

1

2

1

8 =

5

8 =^0 ,^625.