Optimal stopping
Now assume thatr= 100 %and letξuniformly distributed on[ 0 , 1 ]and
letT= 3.
1.t=T= 3 .you have no choice, so your expected payout is
E(ξ 3 )= 1 / 2.
2.t=T 1 = 2 .If
ξ 2 <E(ξ^3 )
1 +r=^1
4
you should continue as in this case your payout is
ξ 2 ( 1 +r)= 2 ξ 2 <E(ξ 3 )= 1 / 2.