Resource extraction with a carbon tax and regime switching prices: Exercising your options

Insley, Margaret

doi:10.1016/j.eneco.2017.07.013

Cited by 22 publications

(11 citation statements)

References 32 publications

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“…[5] and [23]); and in others as a stochastic optimal control problem only with classical absolutely continuous controls (see [1] and [12], among many others), but with commodity price dynamics possibly described by a Markov regime switching model (see, e.g. [21]). The latter kind of dynamics, first introduced by Hamilton [20], may indeed help to explain boom and bust periods of commodity prices in terms of different regimes in a unique stochastic process.…”

Section: Introductionmentioning

confidence: 99%

On an optimal extraction problem with regime switching

Ferrari

Yang

2018

Adv. Appl. Probab.

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This paper studies a finite-fuel two-dimensional degenerate singular stochastic control problem under regime switching that is motivated by the optimal irreversible extraction problem of an exhaustible commodity. A company extracts a natural resource from a reserve with finite capacity, and sells it in the market at a spot price that evolves according to a Brownian motion with volatility modulated by a two-state Markov chain. In this setting, the company aims at finding the extraction rule that maximizes its expected discounted cash flow, net of the costs of extraction and maintenance of the reserve. We provide expressions both for the value function and for the optimal control. On the one hand, if the running cost for the maintenance of the reserve is a convex function of the reserve level, the optimal extraction rule prescribes a Skorokhod reflection of the (optimally) controlled state process at a certain state and price dependent threshold. On the other hand, in presence of a concave running cost function it is optimal to instantaneously deplete the reserve at the time at which the commodity's price exceeds an endogenously determined critical level. In both cases, the threshold triggering the optimal control is given in terms of the optimal stopping boundary of an auxiliary family of perpetual optimal selling problems with regime switching.

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Section: Introductionmentioning

confidence: 99%

On an optimal extraction problem with regime switching

Ferrari

Yang

2018

Adv. Appl. Probab.

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“…28 In addition, SDEs harmonize with the modern mathematical theory of stochastic control, 29 clearly demonstrating that they serve as an appropriate mathematical tool for modeling and control of stochastic system dynamics, as seen in the literature of energy and resource economics. [30][31][32][33] PV systems, which are inherently subject to stochastic weather conditions, would not be an exception.…”

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confidence: 99%

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

Yoshioka

Yano

2019

Appl Stoch Models Bus & Ind

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The operation of a stand‐alone photovoltaic (PV) system ultimately aims for the optimization of its energy storage. We present a mathematical model for cost‐effective control of a stand‐alone system based on a PV panel equipped with an angle adjustment device. The model is based on viscosity solutions to partial differential equations, which serve as a new and mathematically rigorous tool for modeling, analyzing, and controlling PV systems. We formulate a stochastic optimal switching problem of the panel angle, which is here a binary variable to be dynamically controlled under stochastic weather condition. The stochasticity comes from cloud cover dynamics, which is modeled with a nonlinear stochastic differential equation. In finding the optimal control policy of the panel angle, switching the angle is subject to impulsive cost and reduces to solving a system of Hamilton‐Jacobi‐Bellman quasi‐variational inequalities (HJBQVIs). We show that the stochastic differential equation is well posed and that the HJBQVIs admit a unique viscosity solution. In addition, a finite‐difference scheme is proposed for the numerical discretization of HJBQVIs. A demonstrative computational example of the HJBQVIs, with emphasis on a stand‐alone experimental system, is finally presented with practical implications for its cost‐effective operation.

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“…This paper contributes to the literature on optimal natural resource use under uncertainty as exemplied by papers such as Pindyck (1980), Brennan and Schwartz (1985), Mason (2001), Slade (2001), and Chen and Insley (2012), and Insley (2017). It extends the analysis in these papers by including an uncertain regulatory constraint resulting from natural variability in the environment.…”

Section: Introductionmentioning

confidence: 86%

“…Our goals are to determine the best timing for this rm to construct a water storage facility to maximize prots under the water restrictions set by the Framework as well as to explore the marginal cost of the restrictions for a typical rm. The decision model is based on the one developed in Insley (2017), however, the current model includes the constraint on water withdrawals which follows a Poisson process, includes water inventory as an additional state variable, and includes the decision to construct storage as an optimal control.…”

Section: Model Descriptionmentioning

confidence: 99%

The Economics of Water Conservation Regulations Under Uncertainty: An Application to Alberta’s Lower Athabasca River Region

Huang

Insley

2020

SSRN Journal

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Large water demands by the mining industry are of increasing concern around the world. Command and control water regulations may be highly inecient. The cost of a specic command and control water management policy is studied for an oil sands mining operation in Canada, where restrictions on water withdrawals vary with uctuations in the river. A dynamic stochastic optimal control model is specied for a rm choosing production, water use, and the timing to build a water storage facility, under conditions of uncertain oil prices and uncertain water withdrawal limits. A numerical solution of an HJB equation is implemented to determine the dierence in value and optimal controls for the oil-producing asset, with and without water restrictions. The cost of the restrictions is estimated to be quite small given the current reserve base and capacity of the industry. The marginal cost of tightening restrictions is non-monotonic with respect to price volatility.

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Resource extraction with a carbon tax and regime switching prices: Exercising your options

Cited by 22 publications

References 32 publications

On an optimal extraction problem with regime switching

On an optimal extraction problem with regime switching

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

The Economics of Water Conservation Regulations Under Uncertainty: An Application to Alberta’s Lower Athabasca River Region

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