Mathematics for Economists

Optimal stopping

3. Ifξ 1 < 5 /8 then you should not takeξ 1 .Then you expected payout in
   this period

E



max



5

8 ,ξ^1



=

Z 5 / 8

0

5

8 dx+

Z 1

5 / 8

xdx=

=

25

64 +



x^2

2

 1

5 / 8

=

25

64 +

1

2

1

2

25

64 =

=^12 +^126425 =^64128 +^25 = 12889 = 0 ,695 31.