Mathematics for Economists

Optimal stopping

The left side is increasing the right side decrasing soS=fxag,where

ais the solution of the equation

( 1 +r)a=aF(a)+

Z∞

a

xdF(x).

One should sell atT1 if



nmaxT 1 ξn^2 S



=



nmaxT 1 ξna



,

otherwise one should continue. We show that

τ=min



njmax

kn

ξk 2 S



^T=min



njmax

kn

ξka



^T,