Species preservations in an optimal harvest model with random prices

In this paper, we consider an optimal harvest model in which the objective is to maximize the expected return. The unit price of biomass is assumed constant until a random time when the price increases by a given amount. Furthermore, due to obvious environmental protection requirements, it is assumed that the fishery population is bounded from below for all time so as to reduce the danger of species extinction. Clearly, this problem is an optimal control problem in which a random parameter is involved. However, due to its special structure, it is shown that the problem is convertible into a deterministic optimal control problem and hence is solvable by an existing optimal control software package, MISER. The practical implication of several computed results obtained by this approach is discussed. They are also compared with other related results in the literature.