On an optimal harvesting problem

Abstract

Kaplan [1972] treated a harvesting problem as a discrete time stochastic control model with independent disturbances and with decreasing mean value increase depending either on the value or on the age of the asset. We consider the more general model where the mean value increase depends on the value and also on the age. As main result we obtain the existence of optimal control-limit policies with respect to three different natural orders in state space. A basic role play additional convexity and boundedness assumptions. Our findings extend and correct the main result of Kaplan. The paper contains further detailed information about the solution.