Optimal multi-dimensional stochastic harvesting with density-dependent prices

Abstract

We prove a verification theorem for a class of singular control problems which model optimal harvesting with density-dependent prices or optimal dividend policy with capital-dependent utilities. The result is applied to solve explicitly some examples of such optimal harvesting/optimal dividend problems. In particular, we show that if the unit price decreases with population density, then the optimal harvesting policy may not exist in the ordinary sense, but can be expressed as a “chattering policy”, i.e. the limit as Δx and Δt go to 0 of taking out a sequence of small quantities of size Δx within small time periods of size Δt. The final version of this research has been published in Afrika Mathematica. © 2016 Springer Verlag