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).