The expected lifetime of an extraction project

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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. © 2011 The Royal Society.
Original languageEnglish
Pages (from-to)244-263
Number of pages19
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2125
Publication statusPublished - 8 Jan 2011


  • Feynman-Kac
  • Finite resource valuations
  • Real options
  • Stochastic partial differential equations


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