Leif K. Sandal
() and Gerhard Berge
Leif K. Sandal: Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration, Postal: NHH , Department of Finance and Management Science, Helleveien 30, N-5045 Bergen, Norway
Gerhard Berge: Dept. of Mathematics, University of Bergen, Postal: Department of Mathematics, University of Bergen , J. Bruns gt 12, N-5008 Bergen, Norway
Abstract: Dynamic optimization problems cover a great class of problems in theoretical and applied economics and technology. In this account the exploitation of a general renewable capital stock is modeled through an alternative formulation to the classical optimal control approach. We propose a very simple alternating iterative algorithm that is shown to converge very fast towards a solution, where the accuracy of the solution can also be determined. The algorithm can also produce approximate closed form (analytical) feedback solutions. By using a special simple seed in the iteration scheme we reproduce perturbation results (formulae) that are published in the last decade. Often only two or three iteration steps are necessary to produce sufficiently accurate approximations.
21 pages, March 12, 2004
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