Harvesting of a Stochastic Population Under a Mixed Regular-Singular Control Formulation

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 d...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2022-12, Vol.195 (3), p.1106-1132
Main Authors: Tran, Ky Q., Le, Bich T. N., Yin, George
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied mathematics
Approximation
Calculus of Variations and Optimal Control
Optimization
Decision making
Ecosystems
Engineering
Growth models
Markov analysis
Markov chains
Mathematical analysis
Mathematical functions
Mathematics
Mathematics and Statistics
Noise intensity
Operations Research/Decision Theory
Optimization
Theory of Computation
White noise
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Summary: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.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-022-02127-7