The Optimal Harvest from a Multicohort Stock

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Abstract
The study considers the determination of an optimal control over time, in a discrete-time multistate system, with a time-discounted general reward function. A new technique is developed based upon perturbation about a deterministic optimum equilibrium. This gives rise to a linear–quadratic problem in optimization where the quadratic costs come immediately from the original model. The solutions are also applicable to systems subject to an additive stochastic noise. The techniques are applied to some simple models of harvesting and fisheries. It is shown that for some models, and some domain in parameter space, an optimal linear control exists. A change in the character of the control is found in these simple models with changes in the values of the discount rate, time increment, and growth rate. The introduction of costs associated with a change of control increases the size of the domain in which a linear control is optimal.

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