Abstract
This work focuses on optimal harvesting-renewing for a stochastic population. A mixed regular-singular control formulation with a state constraint and regime switching is introduced. The decision-makers either harvest or renew with finite or infinite harvesting/renewing rates. The payoff functions depend on the harvesting/renewing rates. Several properties of the value function are established. The limiting value function as the white noise intensity approaches infinity is identified. The Markov chain approximation method is used to find numerical approximation of the value function and optimal strategies.
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Acknowledgements
The research of Ky Q. Tran was supported by the National Research Foundation of Korea grant funded by the Korea Government (MIST) NRF-2021R1F1A1062361. The research of George Yin was supported in part by the National Science Foundation under Grant DMS-2204240.
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Communicated by Negash G. Medhin.
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Tran, K.Q., Le, B.T.N. & Yin, G. Harvesting of a Stochastic Population Under a Mixed Regular-Singular Control Formulation. J Optim Theory Appl 195, 1106–1132 (2022). https://doi.org/10.1007/s10957-022-02127-7
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DOI: https://doi.org/10.1007/s10957-022-02127-7