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Optimal costless extraction rate changes from a non-renewable resource

Published online by Cambridge University Press:  04 August 2014

G. W. EVATT ,
P. V. JOHNSON ,
P. W. DUCK  and
S. D. HOWELL
G. W. EVATT
Affiliation:
School of Mathematics, University of Manchester, Manchester, M13 9PL, UK email: geoffrey.evatt@manchester.ac.uk
P. V. JOHNSON
Affiliation:
School of Mathematics, University of Manchester, Manchester, M13 9PL, UK email: geoffrey.evatt@manchester.ac.uk
P. W. DUCK
Affiliation:
School of Mathematics, University of Manchester, Manchester, M13 9PL, UK email: geoffrey.evatt@manchester.ac.uk
S. D. HOWELL
Affiliation:
Manchester Business School, University of Manchester, Booth Street West M15 6PB, UK
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Abstract

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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.

Keywords

Real OptionsMiningOptimal ControlDecision under UncertaintySemi-Lagrangian
Type
Papers
Information
European Journal of Applied Mathematics , Volume 25 , Issue 6 , December 2014 , pp. 681 - 705
Copyright
Copyright © Cambridge University Press 2014 

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