Evatt, G. W. and Johnson, P. V. and Duck, P. W. and Howell, S. D. and Moriarty, J.
(2011)
*The Expected Lifetime of an Extraction
Project.*
Proceedings of the Royal Society A, 467 (2125).
pp. 244-263.
ISSN 1471-2946

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## Abstract

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 closed-form 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.

Item Type: | Article |
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Uncontrolled Keywords: | Partial Differential Equations, Finite Resource Valuations, Feynman-Kac, Real Options. |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 18 Feb 2011 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/1584 |

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