The Expected Lifetime of an Extraction Project

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
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:	https://eprints.maths.manchester.ac.uk/id/eprint/1584

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