Optimal Extraction of Nonrenewable Resources When Prices are Uncertain and Costs Cumulate

Cherian, Joseph; Patel, Jayendu; Khripko, Ilya

doi:10.2139/ssrn.70728

Cited by 9 publications

(13 citation statements)

References 22 publications

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“…Indeed, when mine valuations in the presence of uncertainty are considered, a contingent claims approach is typically used (e.g. Brennan & Schwartz 1985;Cherian et al 2000;Evatt et al 2010). The second approach uses hedging arguments to specify the stochastic dynamics of the risk-adjusted commodity price process, and then applies probabilistic methods to obtain a modified Feynman-Kac equation (e.g.…”

Section: Modified Feynman-kac Equationmentioning

confidence: 99%

The expected lifetime of an extraction project

et al. 2010

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When a mining company begins extraction from a finite resource, it does so in the presence of numerous uncertainties. One key uncertainty is the future price of the commodity being extracted, since a large enough drop in price can make a resource no longer cost-effective to extract, resulting in the mine being closed down. By specifying a stochastic price process, and implementing a financial-type model which leads to the use of partial differential equations, this paper creates the framework for efficiently capturing the probability of a mine remaining open throughout its planned extraction period, and derives the associated expected lifetime of extraction. An approximation to the abandonment price is described, which enables a closedform solution to be derived for the probability of operational success and expected lifetime. This approximation compares well with the full solution obtained using a semi-Lagrangian numerical technique.

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Section: Modified Feynman-kac Equationmentioning

confidence: 99%

The expected lifetime of an extraction project

et al. 2010

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“…Indeed, the importance (and complexity) of joining these two forms of decisions has been noted before, e.g. Brennan & Schwartz (1985); Cherian et al (2000); Slade (2001). With this in mind, we have explicitly shown how these two forms of decision can be married together to improve the overall efficiency of an extraction operation.…”

Section: Discussionmentioning

confidence: 69%

“…Indeed, this highlights the significant improvement in valuation which can be expected by combining and optimising irreversible and costless decisions; such a marrying of control strategies is both more representative of industrial practice and has been a long called-for area of investigation within Real Options, e.g. Brennan & Schwartz (1985); Cherian et al (2000); Kamrad & Earnst (2001);Slade (2001). Our final experiment compares two numerical valuations.…”

Section: Optimal Valuation Resultsmentioning

confidence: 94%

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Optimal costless extraction rate changes from a non-renewable resource

et al. 2014

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This paper considers the role of costless decisions relating to the extraction of a non-renewable resource in the presence of uncertainty. We begin by deriving a size scale of the extractable resource, above which the solution to the valuation and optimal control strategy can be described by analytic solutions; we produce solutions for a general form of operating cost function. Below this critical resource size level the valuation and optimal control strategy must be solved by numerical means; we present a robust numerical algorithm that can solve such a class of problem. We also allow for the embedding of an irreversible investment decision (abandonment) into the optimisation. Finally, we conduct experimentation for each of these two approaches (analytical and numerical), and show how they are consistent with one another when used appropriately. The extensions of this paper's techniques to renewable resources are explored.

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“…Por (1.11), o abandono só será vantajoso se o valor do projeto em cada instante de tempo for inferior ao seu valor residual líquido do custo de abandono 15 . Note que, se o custo de abandono for muito alto, o investidor pode preferir manter-se operando mesmo com prejuízo 16 .…”

Section: Opção De Abandonounclassified

Benefícios governamentais e investimentos no setor de petróleo na presença de custos cumulativos: uma análise com base em opções reais

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Optimal Extraction of Nonrenewable Resources When Prices are Uncertain and Costs Cumulate

Cited by 9 publications

References 22 publications

The expected lifetime of an extraction project

The expected lifetime of an extraction project

Optimal costless extraction rate changes from a non-renewable resource

Benefícios governamentais e investimentos no setor de petróleo na presença de custos cumulativos: uma análise com base em opções reais

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