OPTIMAL HARVESTING OF A RANDOMLY FLUCTUATING RESOURCE .1. APPLICATION OF PERTURBATION METHODS

The effect of noise upon optimal harvesting strategies is considered. Whereas deterministic optimal strategies are based upon local considerations, the stochastic strategies must account for global effects. Perturbation methods are applied to obtain approximate solutions to the resulting boundary value problems, for small amounts of noise. Three problems are considered: (1) a single switching point (optimal escapement level), (2) three switching points, and (3) a switching point near a zero of the net growth rate. Approximate formulas are found for the perturbation of the optimal switching points. Qualitative results and interpretations are also provided.