Impulse and Singular Stochastic Control Approaches for Management of Fish-Eating Bird Population

Yaegashi, Yuta; Yoshioka, Hidekazu; Unami, Koichi; Fujihara, Masayuki

doi:10.1007/978-3-030-00473-6_52

Cited by 4 publications

(15 citation statements)

References 6 publications

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“…2 Research Fellow of Japan Society for the Promotion of Science, Tokyo, Japan. 3 Graduate School of Natural Science and Technology, Shimane University, Matsue City, Japan.…”

Section: Appendix Bmentioning

confidence: 99%

“…Management of animal population, such as fishery resources and their predators, is an important ecological problem. Such examples include aquaculture of Plecoglossus altivelis (P. altivelis, Ayu) in Japan [1], extermination of its predator bird Phalacrocorax carbo (P. carbo, Great cormorant) [2,3], agricultural crops damage by a wild boar Sus scrofa in Europe [4], and feeding damage from many insects to soybean seeds [5]. Recently, fisheating bird P. carbo population has been increasing worldwide, such as in Japan [6], Europe [7], North America [8], and Greenland [9].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Yaegashi et al [3] proposed an optimal control model for cost-effective and sustainable management of P. carbo and a candidate of its exact viscosity solution to a HJBQVI. This model has a different performance index from those in the abovementioned literature.…”

Section: Introductionmentioning

confidence: 99%

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An exact viscosity solution to a Hamilton–Jacobi–Bellman quasi-variational inequality for animal population management

et al. 2019

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We formulate a stochastic impulse control model for animal population management and a candidate of exact solutions to a Hamilton-Jacobi-Bellman quasi-variational inequality. This model has a qualitatively different functional form of the performance index from the existing monotone ones. So far, optimality and unique solvability of the Hamilton-Jacobi-Bellman quasi-variational inequality has not been investigated, which are thus addressed in this paper. We present a candidate of exact solutions to the Hamilton-Jacobi-Bellman quasi-variational inequality and prove its optimality and unique solvability within a certain class of solutions in a viscosity sense. We also present and examine a dynamical system-based numerical method for computing coefficients in the exact solutions.

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“…2 Research Fellow of Japan Society for the Promotion of Science, Tokyo, Japan. 3 Graduate School of Natural Science and Technology, Shimane University, Matsue City, Japan.…”

Section: Appendix Bmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An exact viscosity solution to a Hamilton–Jacobi–Bellman quasi-variational inequality for animal population management

et al. 2019

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“…Management problems of population dynamics through harvesting by human have been efficiently described with the impulse control formalism [7] whose control variables are the timing and amount of harvesting. Impulse control models have been applied to various problems, such as predator-prey population management [25], fishery resources management [26], aquaculture operation [27], tree harvesting [28,29], and waterbird management [30]. Deep mathematical analysis of the impulse control models of population dynamics and related models have been carried out [31,32].…”

Section: Introductionmentioning

confidence: 99%

“…The objectives of this paper are formulation and analysis of an impulse control problem of population dynamics subject to imperfect interventions, focusing on its application to a recent waterbird management problem [21,30]. Our model is based on Korn [37], but considers a specific problem where a deeper mathematical and numerical analysis are possible.…”

Section: Introductionmentioning

confidence: 99%

Mathematical and numerical analyses of a stochastic impulse control model with imperfect interventions

Yoshioka

Yaegashi

2021

J.Math.Industry

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A stochastic impulse control problem with imperfect controllability of interventions is formulated with an emphasis on applications to ecological and environmental management problems. The imperfectness comes from uncertainties with respect to the magnitude of interventions. Our model is based on a dynamic programming formalism to impulsively control a 1-D diffusion process of a geometric Brownian type. The imperfectness leads to a non-local operator different from the many conventional ones, and evokes a slightly different optimal intervention policy. We give viscosity characterizations of the Hamilton–Jacobi–Bellman Quasi-Variational Inequality (HJBQVI) governing the value function focusing on its numerical computation. Uniqueness and verification results of the HJBQVI are presented and a candidate exact solution is constructed. The HJBQVI is solved with the two different numerical methods, an ordinary differential equation (ODE) based method and a finite difference scheme, demonstrating their consistency. Furthermore, the resulting controlled dynamics are extensively analyzed focusing on a bird population management case from a statistical standpoint.

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A Stochastic Impulse Control Model for Population Management of Fish-Eating Bird Phalacrocorax Carbo and Its Numerical Computation

Yaegashi

Yoshioka

Unami

et al. 2018

Communications in Computer and Information Science

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Impulse and Singular Stochastic Control Approaches for Management of Fish-Eating Bird Population

Cited by 4 publications

References 6 publications

An exact viscosity solution to a Hamilton–Jacobi–Bellman quasi-variational inequality for animal population management

An exact viscosity solution to a Hamilton–Jacobi–Bellman quasi-variational inequality for animal population management

Mathematical and numerical analyses of a stochastic impulse control model with imperfect interventions

A Stochastic Impulse Control Model for Population Management of Fish-Eating Bird Phalacrocorax Carbo and Its Numerical Computation

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