Optimal harvesting and planting control in stochastic logistic population models

Hiroaki Morimoto

doi:10.3934/dcdsb.2012.17.2545

Article Contents

2012, Volume 17, Issue 7: 2545-2559. Doi: 10.3934/dcdsb.2012.17.2545

This issue Previous Article Interface oscillations in reaction-diffusion systems above the Hopf bifurcation Next Article Kolmogorov's normal form for equations of motion with dissipative effects

Optimal harvesting and planting control in stochastic logistic population models

Hiroaki Morimoto^1,

1.
Department of Economics, Matsuyama University, Matsuyama 790-8578

Received: April 30, 2012

Revised: April 30, 2012

Published: September 2012

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Abstract

We consider the optimal harvesting and planting control problem to maximize the expected total net benefits in the stochastic logistic population model. The variational inequality associated with this problem is given by the degenerate form of elliptic type with quadratic coefficients. Using the viscosity solutions technique, we solve the corresponding penalty equation and show the existence of a solution to the variational inequality. The optimal harvesting and planting policy is characterized in terms of two thresholds for the variational inequality.

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Mathematics Subject Classification: Primary: 90E20, 92A15; Secondary: 60J70.

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