Optimal harvesting and planting control in stochastic logistic population models
Hiroaki Morimoto
Discrete & Continuous Dynamical Systems - B 2012, 17(7): 2545-2559 doi: 10.3934/dcdsb.2012.17.2545
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.
keywords: variational inequality stochastic logistic model viscosity solution. planting Optimal harvesting
A linear-quadratic control problem with discretionary stopping
Shigeaki Koike Hiroaki Morimoto Shigeru Sakaguchi
Discrete & Continuous Dynamical Systems - B 2007, 8(2): 261-277 doi: 10.3934/dcdsb.2007.8.261
We study the variational inequality for a 1-dimensional linear-quadratic control problem with discretionary stopping. We establish the existence of a unique strong solution via stochastic analysis and the viscosity solution technique. Finally, the optimal policy is shown to exist from the optimality conditions.
keywords: Viscosity solution stopping time linear-quadratic control.

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