Optimal harvesting with exponential growth in an environment with random disasters and bonanzas
type: Item
instance of: scholarly article
title: Optimal harvesting with exponential growth in an environment with random disasters and bonanzas
zbMATH Open document ID: 0568.92019
DOI: 10.1016/0025-5564(85)90024-0
author: Dennis Ryan
author: Floyd B. Hanson
published in: Mathematical Biosciences
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 90B99
zbMATH DE Number: 3908228
zbMATH Keywords: optimal harvesting
zbMATH Keywords: exponential growth
zbMATH Keywords: random bonanzas
zbMATH Keywords: optimal discounted present value of an exploited population
zbMATH Keywords: constant effort harvesting
zbMATH Keywords: random disasters
zbMATH Keywords: Malthusian
zbMATH Keywords: Poisson process
zbMATH Keywords: density independent properties
zbMATH Keywords: constant effort open loop policy
zbMATH Keywords: exact solution for the expected present value
zbMATH Keywords: average random jump model
zbMATH Keywords: deterministic jump model
MaRDI profile type: Publication
full work available at URL: 0025-5564(85)90024-0
OpenAlex ID: W2060879245
cites work: Q4139908
cites work: Mathematical Models in the Economics of Renewable Resources
cites work: A mathematical theory for the harvest of natural animal populations when birth rates are dependent on total population size
cites work: A discrete time population control model
cites work: A stochastic model for the economic management of a renewable animal resource
cites work: A systematic approach to determining mean-variance tradeoffs when managing randomly varying populations
cites work: Optimal harvesting in continuous time with stochastic growth
cites work: Optimal Harvesting of a Randomly Fluctuating Resource. I: Application of Perturbation Methods
cites work: Persistence times of populations with large random fluctuations
cites work: Logistic growth with random density independent disasters
cites work: Q3960440
cites work: Q5653395
cites work: Q4109064
cites work: Q4134790
cites work: Q3317025
cites work: Analysis of a singular functional differential equation that arises from stochastic modeling of population growth
description: scientific article; zbMATH DE number 3908228