Optimal harvesting of a logistic population in an environment with stochastic jumps

Journal of Mathematical Biology
D Ryan, F B Hanson

Abstract

Dynamic programming is employed to examine the effects of large, sudden changes in population size on the optimal harvest strategy of an exploited resource population. These changes are either adverse or favorable and are assumed to occur at times of events of a Poisson process. The amplitude of these jumps is assumed to be density independent. In between the jumps the population is assumed to grow logistically. The Bellman equation for the optimal discounted present value is solved numerically and the optimal feedback control computed for the random jump model. The results are compared to the corresponding results for the quasi-deterministic approximation. In addition, the sensitivity of the results to the discount rate, the total jump rate and the quadratic cost factor is investigated. The optimal results are most strongly sensitive to the rate of stochastic jumps and to the quadratic cost factor to a lesser extent when the deterministic bioeconomic parameters are taken from aggregate antarctic pelagic whaling data.

References

Aug 1, 1978·Theoretical Population Biology·F B Hanson
Jan 1, 1976·Toxicon : Official Journal of the International Society on Toxinology·M D Owen, A R Bridges
Jan 1, 1982·Archives of Virology·W Rohde
Jul 29, 1977·Science·J R Beddington, R M May

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Citations

Mar 1, 1989·Mathematical Biosciences·F B Hanson, D Ryan
Aug 1, 1989·Mathematical Biosciences·C J Goh, K L Teo
Jun 4, 1998·Mathematical Biosciences·F B Hanson, D Ryan
Feb 6, 2016·Journal of Mathematical Biology·Meng Liu, Chuanzhi Bai
Apr 5, 2018·Journal of Biological Dynamics·Xin-You MengHai-Feng Huo

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