Mathematics for Economists

Stochastic dynamic programming

In the Örst optimal stopping problem above introduce a special statex

fk(xk,uk,ξk) $

8

<

:

x if xk=x

x if xk 6 =x,uk=stop

ξk otherwise

g(xT) $



xT if xT 6 =x

0 otherwise

uk(xk,uk,ξk) $



ξk( 1 +r)Tk if xk 6 =x,uk=stop

0 otherwise

U(xk) $



∅ if xk=x

fstop,continueg otherwise