Mathematics for Economists

Optimal control

Asp(t)>0 for everyt 2 ( 0 , 1 )the max of the

H(t,x,u,p)=x+p(x+u)overu 2 [ 1 , 1 ]isu(t) 1 .As

x(t)=x(t)+u(t)=x(t)+ 1.

It is again linear the general solution is

x(t)=Cet 1.

Using the initial conditionx( 0 )= 0 C=1, so the optimal solution is

x(t)=exp(t) 1.