Optimal stopping
Letξtbe exponentialλ= 1 .The backward iteration is withαT= 0
αt = E(max(αt+ 1 ,ξt))=
Zαt+ 1
0
αt+ 1 exp( x)dx+
Z∞
αt+ 1
xexp( x)dx=
= αt+ 1
Zαt+ 1
0
exp( x)dx+
xexp( x)
1
∞
αt+ 1
+
Z∞
αt+ 1
exp( x)dx=
= αt+ 1 ( 1 exp( αt+ 1 ))+αt+ 1 exp( αt+ 1 )+exp( αt+ 1 )=
= αt+ 1 +exp( αt+ 1 ).