Verification Theory and Approximate Optimal Harvesting Strategy for a Stochastic Competitive Ecosystem Subject to Lévy Noise

Verification Theory and Approximate Optimal Harvesting Strategy for a Stochastic Competitive... This work focuses on optimal harvesting problems for a stochastic competitive ecosystem subject to Lévy noise. A verification theorem for corresponding harvesting strategy is established, which offers sufficient conditions for deriving an optimal harvesting strategy and an upper bound of the value function. For a given instantaneous marginal yields function, a concrete upper bound of value function is constructed by applying the verification theorem obtained in this paper. Meanwhile, the monotonicity of value function is investigated. Also, an ε-optimal harvesting strategy is designed to find an approximate optimal harvesting strategy for those harvesting problems with no exact optimal harvesting strategy. Finally, by choosing appropriately Markov decision process defined on a discrete state space, a computational method for an optimal harvesting strategy is designed and a concrete example is also given to show the implementation of the algorithm. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Dynamical and Control Systems Springer Journals

Verification Theory and Approximate Optimal Harvesting Strategy for a Stochastic Competitive Ecosystem Subject to Lévy Noise

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media New York
Subject
Engineering; Vibration, Dynamical Systems, Control; Calculus of Variations and Optimal Control; Optimization; Analysis; Applications of Mathematics; Systems Theory, Control
ISSN
1079-2724
eISSN
1573-8698
D.O.I.
10.1007/s10883-017-9362-y
Publisher site
See Article on Publisher Site

Abstract

This work focuses on optimal harvesting problems for a stochastic competitive ecosystem subject to Lévy noise. A verification theorem for corresponding harvesting strategy is established, which offers sufficient conditions for deriving an optimal harvesting strategy and an upper bound of the value function. For a given instantaneous marginal yields function, a concrete upper bound of value function is constructed by applying the verification theorem obtained in this paper. Meanwhile, the monotonicity of value function is investigated. Also, an ε-optimal harvesting strategy is designed to find an approximate optimal harvesting strategy for those harvesting problems with no exact optimal harvesting strategy. Finally, by choosing appropriately Markov decision process defined on a discrete state space, a computational method for an optimal harvesting strategy is designed and a concrete example is also given to show the implementation of the algorithm.

Journal

Journal of Dynamical and Control SystemsSpringer Journals

Published: Mar 20, 2017

References

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