Mathematics for Economists

Optimal stopping

The expected gain with this strategy

( 1 +r)E



max



1

4

,ξ 2



= 2

Z 1 / 4

0

1

4

dx+

Z 1

1 / 4

xdx



=

=^1

8

+ 2



x^2

2

 1

1 / 4

=^1

8

+ 1 ^1

16

=^17

16

=

=^1

4

^1

2

+^3

4

2
^5

8

=

=^1

4

E(ξ 3 )+^3

4

( 1 +r)
^5

8

.

Where 5/8 is the expected value of the uniform distribution on[ 1 / 4 , 1 ].