Mathematics for Economists

Optimal stopping

3. If( 1 +r)^2 ξ 1 < 17 /16, that is ifξ 1 < 17 /64 you should continue.
   Your expected gain is

(^1 +r)^2 E



max



17

64

,ξ 1



= 4

Z 17 / 64

0

17

64

dx+

Z 1

17 / 64

xdx



=

= 4

(^) 
17
64

 2

+^12

1



17

64

 2 !!

=

=

17

64

17

16 +^2

1



17

64

 2!

=

4385

2048