Abstract
A new stochastic optimal control approach is introduced which quantifies the risk of extinction of a population associated with its optimal exploitation. In addition the maximization of the profit can be performed subject to the constraint that the mentioned risk does not exceed a given limit. As a first example for this general method an exponentially growing population is investigated. The interdependence of the risk and the profit is discussed. This model reveals the possibility of reducing the risk considerably without a substantial decrease of profit.
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