Adv. Math. Econ. 10, 65-89 (2007)

Golden optimal policy in calculus of variation and dynamic programming

Seiichi Iwamoto

Department of Economic Engineering, Graduate School of Economics, Kyushu University, Fukuoka 812-8581, Japan

Received: April 22, 2006 Revised: September 12, 2006

JEL classification: C61, D81

Mathematical Subject Classification (2000): 90C39, 90C40, 90A43

Abstract. This paper discusses four dynamic optimization problems on an infinite continuous time interval from a viewpoint of Golden optimality. The problem is whether an optimal policy is Golden or not. We solve two control processes with quadratic cost criterion and two allocation processes with discounted square-root reward criterion. Both processes have a linear dynamics. It is shown that one cotrol process does not admit a Golden optimal policy. The other three processes have a Golden optimal policy. Further we illustrate the Golden optimal trajectories through three approaches: (i) one-parametric method, (ii) Euler equation and (iii) Bellman equation.

Key words: golden policy, optimal policy, Euler equation, Bellman equation, golden optimality, control process, allocation process, golden section