[Advanced Project] In this chapter we used calculus of variations as the main tool for solving our lifecycle model. In this project we look at an alternative approach, based on the principle of optimality under the framework of dynamic optimization (programming).

Principle of Optimality. Here we establish the main theorem by considering the following generic problem

Transcribed Image Text:

max So C a (t, c) dt + (zb) subject to += f(t, Ct, Zt), for given functions o, f, and . Define a value function V(t, z+) as V(t, z+) = max and we have the following results. Za = z b (s, cs)ds + V (Zb) Theorem. Let c be the optimal control, and z be the resulting state of the control problem. For a < t