Scandinavian Working Papers in Economics

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2009/8: Approximating Closed Form Solutions to a Class of Feedback Policies

Leif K. Sandal ()
Additional contact information
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

Abstract: Dynamic optimization problems cover a large class of problems in theoretical and applied economics. A simple iterative algorithm with fast convergence is proposed. It is demonstrated that the algorithm in a few steps produce excellent analytic (closed form) approximations including error bounds to a class of nonlinear problems. The algorithmic scheme is also well suited to produce numerical solutions. The notions of dynamic and potential rents are operationalized. The algorithm is utilizing a relation balancing these concepts. The result is particularly strong in the case of zero discounting where the exact CU-optimal policy is determined in a single step. Applying a particular seed in the general convergent scheme reproduces in a simple way results (formulas) published in the last decade in bioeconomics.

Keywords: Closed form approximations; Contraction algorithm; Renewable resource economics; Capital dynamic modeling; Zero discounting and optimality

JEL-codes: A12; C61; C63; E10; Q00

27 pages, September 15, 2009

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