Optimal harvesting with exponential growth in an environment with random disasters and bonanzas
The optimal discounted present value of an exploited population under constant effort harvesting in an environment with random disasters and bonanzas is investigated. The deterministic component of growth is density independent (also called Malthusian or exponential). The disasters and bonanzas are random, occurring at the times of events of a Poisson process. The density independent properties of the model and the constant effort open loop policy lead to an exact solution for the expected present value. The optimal expected present value is compared with those in deterministic models with and without deterministic type jumps. Both deterministic and random jumps can have a significant influence on the optimal present value. However, the effort to achieve the optimal is not sensitive to variations in the total jump frequency or in the discount rate. The average random jump model is much easier to apply than the deterministic jump model. Bonanzas can have much more of an effect on the present value than disasters given similar jump rates.
optimal discounted present value of an exploited population
exact solution for the expected present value
scientific article; zbMATH DE number 3908228
scientific article