Optimal control of a renewable natural resources and the “stochastically induced critical depensation”

This paper focus aspects connected to the optimal control of a renewable resource modelled by a stochastic differential equation. The main point is to show how small changes of the problem may cause severe changes in the properties of the control. In particular we show how the introduction of uncertainty may lead to a less conservative policy. In this context we introduce the notion “induced critical depensation”. We also demonstrate how a stochastic process may be analysed by comparison with a simpler process. ∗Institute of Finance and Management Science, Norwegian School of Economics and Business Administration, Helleveien 30, 5045 Bergen, Norway. Email [email protected]. The author wish to thank Leif K. Sandal for valuable comments.