Mathematics for Economists

Optimal stopping

IfF(x)is the distribution function of(ξn)then the optimal exercise

boundary is

αT = 0 ,

αt = E(Vk+^1 (ξt))

1 +r

=

E(max(ξt+ 1 ,αt+ 1 ))

1 +r

=

=^1

1 +r

Zαt+ 1

0

αk+ 1 dF+

Z∞

αt+ 1

xdF(x)



=

=

1

1 +r



αt+ 1 F(αt+ 1 )+

Z∞

αt+ 1

xdF(x)



.

which is a backward induction for(αt).