Mathematics for Economists

Optimal control, Bolza problem

d

dt

ep(t)= d

dt

p(t)+φ^00 (x(t))x(t).

Hence

d

dtep(t)=

fx^0 +epgx^0

,p(T)= 0.

IfHe=f+epgthen

d

dtep(t)=

Hex^0 , ep=φ^0 (x(T)).