Optimal stopping
The general iteration isαT= 0.αt = E(max(αt+ 1 ,ξt))=Zαt+ 1
0αt+ 1 dx+Z 1
αt+ 1xdx== α^2 t+ 1 +1
2
1 α^2 t+ 1=
1
2
1 +α^2 t+ 1.
Obviously from the constructionαt>αt+ 1 as we are always increasing
the integrand.
Is this the optimal strategy?