Optimal costless extraction rate changes from a non-renewable resource

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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.
Original languageEnglish
Pages (from-to)681-705
Number of pages24
JournalEuropean Journal of Applied Mathematics
Issue number6
Publication statusPublished - 4 Aug 2014


  • Decision under Uncertainty
  • Mining
  • Optimal Control
  • Real Options
  • Semi-Lagrangian
  • Resource extraction
  • stochastic ore grades
  • optimal extraction rates


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