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An optimal hunting policy for a stochastic logistic model

Published online by Cambridge University Press:  14 July 2016

Andris Abakuks
Andris Abakuks*
Affiliation:
Birkbeck College, London
*
∗Postal address: Department of Statistics, Birkbeck College, Malet St., London WCIE 7HX, U.K.
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Abstract

A stochastic version of the logistic model for population growth is considered, and the general form of an optimal policy is found for hunting the population so as to maximise the long-term average number of captures per unit time. This optimal policy is described by a critical population size x∗such that it is optimal to hunt if and only if the population size is greater than or equal to x∗. Methods of determining x∗for given parameter values are provided, and some properties of the optimal policy as the population size tends to infinity are proved.

Keywords

STOCHASTIC LOGISTIC MODELOPTIMAL HUNTINGMARKOV DECISION PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 2 , June 1979 , pp. 319 - 331
Copyright
Copyright © Applied Probability Trust 1979 

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References

Bailey, N. T. J. (1950) A simple stochastic epidemic. Biometrika 37, 193–202.CrossRefGoogle ScholarPubMed
Bather, J. (1976) Optimal stationary policies for denumerable Markov chains in continuous time. Adv. Appl. Prob. 8, 144–158.CrossRefGoogle Scholar
Conway, G. R. (1977) Mathematical models in applied ecology. Nature (London) 269, 291–297.CrossRefGoogle Scholar
Howard, R. A. (1960) Dynamic Programming and Markov Processes. Wiley, New York.Google Scholar
Miller, B. L. (1968) Finite state continuous time Markov decision processes with an infinite planning horizon. J. Math. Anal. Appl. 22, 552–569.CrossRefGoogle Scholar