Mathematics for Economists

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 ).