Journal Article

Risk-sensitive optimal harvesting and control of biological populations

J. W. HORWOOD

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 13, issue 1, pages 35-71
Published in print March 1996 | ISSN: 1477-8599
e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/13.1.35
Risk-sensitive optimal harvesting and control of biological populations

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Theory recently developed elsewhere is introduced, to a more applied and biological audience, for the optimal control of linear systems with a risk-sensitive exponential of a quadratic (LEQG) cost function, and for the optimal control of fully nonlinear systems through the risk-sensitive maximum principle (RSMP). The LEQG theory is extended, in this study, to give solutions for locally optimal stochastic control of nonlinear systems. Examples and applications are given of the extended theory, using simple, heuristic logistic models and more complex multicohort models of fisheries. Implementations of the nonlinear RSMP are described. The results show how the theories can be applied to biological harvesting and control problems. They also shed some light upon the character of the dynamics of the risk-sensitive optimal solutions, which have been little explored.

Keywords: population dynamics; resource management; fisheries; risk

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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