Stochastic dynamic programming

DeÖnition

Stochastic dynamic programming problem on Önite time horizon is

E

g(xT)+

T 1

∑

k= 0

uk(xk,uk,ξk)

!

!max

xk+ 1 =fk(xk,uk,ξk),uk 2 Uk(xk),k= 0 , 1 ,.. .,T 1

x 0 =a;

The value of the optimum isJ(x 0 ).