Mathematics for Economists

Optimal stopping

Xt

( 1 +r)Tt

= max(ξt,αt).

Vt(ξt) $

Xt

( 1 +r)Tt

=

( 1 +r)Ttmax(ξt,αt)

( 1 +r)Tt

=max(ξt,αt),

αt $ E(Xt+^1 )

( 1 +r)Tt

= 1 +^1 r E(Xt+^1 )

( 1 +r)T(t+^1 )

=E(V 1 t++^1 r(ξ)).

Hence

Vt(ξt)=max(ξt,αt)=max



ξt,

E(Vt+ 1 (ξt))

1 +r



.