Risk-sensitive optimal harvesting and control of biological populations

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.