Regulation of Renewable Resource Exploitation

Kharroubi, Idris; Lim, Thomas; Mastrolia, Thibaut

doi:10.1137/19m1265740

Cited by 8 publications

(10 citation statements)

References 20 publications

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“…In other words, the bounded rate at which the species can be harvested or renewed is proportional and positively related to the current size. Such a consideration is motivated by the observations in [1, Section 3] and [14].…”

Section: Formulationmentioning

confidence: 99%

“…In [7,8], the authors study ecosystems that allow for the modelling of both renewing and harvesting. Optimal exploitation problems of renewable natural resources, which are harvesting-type problems, are studied in [14,27]. Related works on a general one-dimensional diffusion that is reflected at zero can be found in [4] and references therein.…”

Section: Introductionmentioning

confidence: 99%

“…renewing rates); see [1,7,8]. In [14,27], interesting phenomena appear when the control objective is taken into account. For instance, the maximal possible rates are no longer optimal for harvesting and renewing in certain cases.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Harvesting of a stochastic population under a mixed regular-singular control formulation

Tran

Bich

Yin

2021

Preprint

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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 functions 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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Section: Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Harvesting of a stochastic population under a mixed regular-singular control formulation

Tran

Bich

Yin

2021

Preprint

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“…Then, applying a dynamic programming principle 2 reduces the control problem to a degenerate parabolic or elliptic equation, called the Hamilton-Jacobi-Bellman equation (HJBE), from which the optimal control would be found. Solving the HJBE is in general carried out either analytically [15][16][17] or numerically. [18][19][20] The conventional framework assumes that the decision-maker controlling the target dynamics can receive complete information of the dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…Then, applying a dynamic programming principle [2] reduces the control problem to a degenerate parabolic or elliptic equation, called the optimality equation, from which the optimal control would be found. Solving the optimality equation is in general carried out either analytically [15][16][17] or numerically [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Stochastic impulse control of nonsmooth dynamics with partial observation and execution delay: Application to an environmental restoration problem

Yoshioka

Yaegashi²

2021

Optim Control Appl Methods

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Nonsmooth dynamics driven by stochastic disturbance arise in a wide variety of engineering problems. Impulsive interventions are often employed to control stochastic systems; however, the modeling and analysis subject to execution delay have been less explored. In addition, continuously receiving information of the dynamics is not always possible. In this article, with an application to an environmental restoration problem, a continuous-time stochastic impulse control problem subject to execution delay under discrete and random observations is newly formulated and analyzed. The dynamics have a nonsmooth coefficient modulated by a Markov chain, and eventually attain an undesirable state like a depletion due to the nonsmoothness. The goal of the control problem is to find the most cost-efficient policy that can prevent the dynamics from attaining the undesirable state. We demonstrate that finding the optimal policy reduces to solving a nonstandard system of degenerate elliptic equations, the Hamilton-Jacobi-Bellman equation (HJBE), which is rigorously and analytically verified in a simplified case. The associated Fokker-Planck equation (FPE) for the controlled dynamics is derived and solved explicitly as well. The model is finally applied to numerical computation of a recent river environmental restoration problem. The HJBE and FPE are successfully computed, and the optimal policy and the probability density functions are numerically obtained.The impacts of execution delay are discussed to deeper analyze the model.

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Incentives, lockdown, and testing: from Thucydides’ analysis to the COVID-19 pandemic

et al. 2022

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In this work, we provide a general mathematical formalism to study the optimal control of an epidemic, such as the COVID-19 pandemic, via incentives to lockdown and testing. In particular, we model the interplay between the government and the population as a principal–agent problem with moral hazard, à la Cvitanić et al. (Finance Stoch 22(1):1–37, 2018), while an epidemic is spreading according to dynamics given by compartmental stochastic SIS or SIR models, as proposed respectively by Gray et al. (SIAM J Appl Math 71(3):876–902, 2011) and Tornatore et al. (Phys A Stat Mech Appl 354(15):111–126, 2005). More precisely, to limit the spread of a virus, the population can decrease the transmission rate of the disease by reducing interactions between individuals. However, this effort—which cannot be perfectly monitored by the government—comes at social and monetary cost for the population. To mitigate this cost, and thus encourage the lockdown of the population, the government can put in place an incentive policy, in the form of a tax or subsidy. In addition, the government may also implement a testing policy in order to know more precisely the spread of the epidemic within the country, and to isolate infected individuals. In terms of technical results, we demonstrate the optimal form of the tax, indexed on the proportion of infected individuals, as well as the optimal effort of the population, namely the transmission rate chosen in response to this tax. The government’s optimisation problems then boils down to solving an Hamilton–Jacobi–Bellman equation. Numerical results confirm that if a tax policy is implemented, the population is encouraged to significantly reduce its interactions. If the government also adjusts its testing policy, less effort is required on the population side, individuals can interact almost as usual, and the epidemic is largely contained by the targeted isolation of positively-tested individuals.

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Regulation of Renewable Resource Exploitation

Cited by 8 publications

References 20 publications

Harvesting of a stochastic population under a mixed regular-singular control formulation

Harvesting of a stochastic population under a mixed regular-singular control formulation

Stochastic impulse control of nonsmooth dynamics with partial observation and execution delay: Application to an environmental restoration problem

Incentives, lockdown, and testing: from Thucydides’ analysis to the COVID-19 pandemic

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