Optimal Consumption and Exploration of Nonrenewable Resources under Uncertainty

Deshmukh, S. D.; Pliska, Stanley R.

doi:10.2307/1912024

Cited by 76 publications

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“…Such a model has been studied in detail in [DP80,Son85]. Relative to the analysis of the previous section, this model is both more difficult (since we now have a two-dimensional continuous control to deal with) and simpler (since there are no longer any free boundaries).…”

Section: Continuous Exploration Controlmentioning

confidence: 99%

“…In the monopoly setting the marginal value of additional reserves v ′ has a natural interpretation as the scarcity value of the resource. We recall the stochastic Hotelling theorem of [DP80] which studies the evolution of this value over time. Let…”

Section: Marginal Value Of Reserves Dynamicsmentioning

confidence: 99%

“…A series of works extended Pindyck's model for the case of stochastic discoveries. If exploration is punctuated by large discoveries, it is best represented as a point process [DP80,AC82,Son85,HWCK94]. This is the point of view we take in this paper.…”

Section: Introductionmentioning

confidence: 99%

“…This is the point of view we take in this paper. In particular, the model of [DP80,AC82] essentially matches our monopoly setup with continuous effort in Section 2.3, except that we interpret value of production q as revenue P (q) · q, whereas the existing works simply interpret it as utility of consumption u(q).…”

Section: Introductionmentioning

confidence: 99%

“…If the global resource is finite, like in the case of hydrocarbons, over the long term total possible discoveries are bounded and exploration becomes harder as time goes on, see [Pin78]. In this paper, again as in [DP80], we make the simpler assumption that exploration can go on forever, which is akin to unbounded technological R&D and knowledge accumulation. This implies that the controlled reserves process (X * t ) in our model is recurrent on (a subset of) R + and moreover that zero is recurrent for (X * t ) (i.e.…”

Section: Introductionmentioning

confidence: 99%

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Exploration and exhaustibility in dynamic Cournot games

Ludkovski

Sircar

2011

Eur. J. Appl. Math

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We study the stochastic effect of resource exploration in dynamic Cournot models of exhaustible resources, such as oil. We first treat the case of a monopolist who may undertake costly exploration to replenish his diminishing reserves. We then consider a stochastic game between such an exhaustible producer and a "green" producer that has access to an inexhaustible but relatively expensive source, such as solar power. The effort control variable is taken to be either continuous or discrete (switching control). In both settings, we assume that new discoveries occur according to a jump process with intensity given by the exploration effort. This leads to a study of systems of nonlinear first order delay ODEs. We derive asymptotic expansions for the case of a small exploration success rate and present some numerical investigations.

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Section: Continuous Exploration Controlmentioning

confidence: 99%

Section: Marginal Value Of Reserves Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exploration and exhaustibility in dynamic Cournot games

Ludkovski

Sircar

2011

Eur. J. Appl. Math

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Approximation of integro-differential equations associated with piecewise deterministic process

Camilli

1997

Optim. Control Appl. Meth.

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Aim of this paper is to present an approximation scheme for optimal control problems of piecewise deterministic processes and corresponding integro‐differential Hamilton–Jacobi–Bellman equations. The method is based on a discrete dynamic programming approach. We discretize the continuous process and the cost functional obtaining a discrete time optimal control problem. The corresponding dynamic programming equation gives an approximation of the integro‐differential equation. The main feature of the method is the uniform convergence to the value function of the continuous control problem, which can be characterized as the unique weak solution (in viscosity sense) of the dynamic programming equation. Moreover, under appropriate assumptions, an error estimate on the truncation error is derived. It is worth noting that the method provides approximate feedback controls at any point of the grid without extra computations. An application of the approximation scheme to the numerical solution of an optimal control problem for a storage process is also detailed. © 1997 John Wiley & Sons, Ltd.

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Optimal resource extraction with uncertain reserves

Lipshutz¹,

Stone²

1992

Naval Research Logistics

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We consider the problem of finding a plan that maximizes the expected discounted return when extracting a nonrenewable resource having uncertain reserves. An extraction plan specifies the rate at which the resource is extracted as a function of time until the resource is exhausted or the time horizon is reached. The return per unit of resource extracted may depend on the rate of extraction, time, and the amount of resource previously extracted. We apply a new method called the generalized search optimization technique to find qualitative features of optimal plans and to devise algorithms for the numerical calculation of optimal plans.

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Optimal Consumption and Exploration of Nonrenewable Resources under Uncertainty

Cited by 76 publications

References 0 publications

Exploration and exhaustibility in dynamic Cournot games

Exploration and exhaustibility in dynamic Cournot games

Approximation of integro-differential equations associated with piecewise deterministic process

Optimal resource extraction with uncertain reserves

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