Mathematics for Economists

Dynamic programming

1. First let us Önd the solution of the problem att=T.In this case the
   state variable is the wealthw the correspondence

Φ(w)=[ 0 ,w].

Asu(c)=

p

cthe value function at timeTis

VT(w)=maxfu(c)jc 2 Φ(T)g=

p

w.

The optimal strategy is

σT(w)=w.