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

Abstract: Dynamic optimization encompasses a wide range of research questions in both theoretical and applied economics. This paper presents a simple, fast-converging iterative scheme capable of generating highquality analytic (closed-form) approximations—including explicit error bounds—for a class of nonlinear problems. The algorithm is also well-suited for producing numerical solutions. We define and operationalize the concepts of dynamic rents and potential rents, and show how our approach leverages a balancing relation between these rents to derive optimal policies. A powerful result emerges for zero discounting, where the exact Catching-up optimal policy is obtained in a single iteration. By applying a specific initial seed within our general framework, it recovers known results from the bioeconomics literature, illustrating the constructive nature of our theorem and the versatility of the procedure. It provides previously unavailable error bounds, enhancing both their theoretical robustness and practical applicability.

Keywords: Dynamic and potential rents; Renewable resource economics; Closed form approximations; Capital dynamic modeling; Zero discounting and optimality

JEL-codes: C60; C61; Q20

Language: English

29 pages, June 8, 2026

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