Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-08T00:20:20.682Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
P. V. JOHNSON
Affiliation:
School of Mathematics, University of Manchester, Manchester, M13 9PL, UK email: [email protected]
P. W. DUCK
Affiliation:
School of Mathematics, University of Manchester, Manchester, M13 9PL, UK email: [email protected]
S. D. HOWELL
Affiliation:
Manchester Business School, University of Manchester, Booth Street West M15 6PB, UK
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 

References

Ahn, C., Choe, H. J. & Lee, K. (2006) A long time asymptotic behaviour for an american put. Proc. Am. Math. Soc. 137 (10), 3425–3436.Google Scholar
Atkinson, C. & Isangulov, R. (2010) A mathematical model of an oil and gas field development process. Euro. J. Appl. Math. 21 (03), 205–227.Google Scholar
Benchekroun, H., Halsema, A. & Withagen, C. (2009) On nonrenewable resource oligopolies: The asymmetric case. J. Econ. Dyn. Control 33 (11), 1867–1879.CrossRefGoogle Scholar
Brennan, M. J. (1958) The supply of storage. Am. Econ. Rev. 48 (1), 50–72.Google Scholar
Brennan, M. J. & Schwartz, E. (1985) Evaluating natural resource investments. J. Bus. 58 (2), 135–157.CrossRefGoogle Scholar
Chen, Z. & Forsyth, P. (December 2007) A semi-lagrangian approach for natural gas storage valuation and optimal operation. SIAM J. Sci. Comput. 30, 339–368.Google Scholar
Cherian, J. A., Patel, J. & Khripko, I. (2000) Optimal extraction of nonrenewable resources when costs cumulate. In: Brennan, M. J. & Trigeorgis, L. (editors), Project flexibility, agency, and competition, Oxford University Press, New York, pp. 224–253.Google Scholar
Cortazar, G., Schwartz, E. S. & Salinas, M. (1998) Evaluating environmental investments: A real options approach. Manage. Sci. 44 (8), 1059–1070.Google Scholar
Dehghani, H. & Ataee-pour, M. (2012) Determination of the effect of operating cost uncertainty on mining project evaluation. Resour. Policy 37 (1), 109–117.Google Scholar
Deloitte (2011) Tracking the trends 2011. The top 10 issues mining companies will face in the coming year. Company report. http://www.deloitte.com/view/en_CA/ca/industries/energyandresources/mining/efaa39766789c210VgnVCM3000001c56f00aRCRD.htmGoogle Scholar
Dimitrakopoulos, R. G. & Sabour, S. A. A. (2007) Evaluating mine plans under uncertainty: Can the real options make a difference? Resour. Policy 32 (3), 116–125.CrossRefGoogle Scholar
Dixit, A. & Pindyck, R. (1994) Investment Under Uncertainty. Princeton University Press, New Jersey.Google Scholar
Dominy, S. C., Noppe, M. A. & Annels, A. E. (2002) Errors and uncertainty in mineral resource and ore reserve estimation: The importance of getting it right. Explor. Min. Geol. 11 (1–4), 77–98.Google Scholar
Evatt, G. W., Johnson, P., Duck, P., Howell, S. & Moriarty, J. (2011) The expected lifetime of an extraction project. Proc. R. Soc. A: Math., Phys. Eng. Sci. 467, 244–263.CrossRefGoogle Scholar
Evatt, G. W., Soltan, M. O. & Johnson, P. V. (2012) Mineral reserves under price uncertainty. Resour. Policy 37, 340–345.Google Scholar
Hanemann, W. (1989) Information and the concept of option value. J. Environ. Econ. Manage. 16 (1), 23–37.Google Scholar
Kamrad, B. & Earnst, R. (2001) An economic model for evaluating mining and manufacturing ventures with output yield uncertainty. Oper. Res. 49 (5), 690–699.Google Scholar
McCarthy, J. & Monkhouse, H. L. (2002) To open or not to open: Or what to do with a closed copper mine. J. Appl. Corp. Finance 15, 63–73.Google Scholar
Moel, A. & Tufano, P. (2002) When are real options exercised? An empirical study of mine closings. Rev. Financ. Stud. 15 (1), 35–64.CrossRefGoogle Scholar
Morck, R., Schwartz, E. & Stangeland, D. (1989) The valuation of forestry resources under stochastic prices and inventories. J. Financ. Quant. Anal. 24 (04), 473–487.CrossRefGoogle Scholar
Nøstbakken, L. (2006) Regime switching in a fishery with stochastic stock and price. J. Environ. Econ. Manage. 51 (2), 231–241.CrossRefGoogle Scholar
Øksendal, B. (2003) Stochastic Differential Equations: An Introduction with Applications. Universitext (1979). Springer, Berlin, Germany.Google Scholar
Pindyck, R. (1988) Irreversible investment, capacity choice, and the value of the firm. Am. Econ. Rev. 78 (5), 969–985.Google Scholar
Provencher, B. (1995) Structural estimation of the stochastic dynamic decision problems of resource users: An application to the timber harvest decision. J. Environ. Econ. Manage. 29 (3), 321–338.Google Scholar
Roseta-Palma, C. & Xepapadeas, A. (2004) Robust control in water management. J. Risk Uncertain. 29, 21–34.Google Scholar
Sarkar, S. (2000) On the investmentuncertainty relationship in a real options model. J. Econ. Dyn. Control 24 (2), 219–225.Google Scholar
Schulze, W. D. (1974) The optimal use of non-renewable resources: The theory of extraction. J. Environ. Econ. Manage. 1 (1), 53–73.CrossRefGoogle Scholar
Schwartz, E. (1997) The stochastic behavior of commodity prices: Implications for valuation and hedging. J. Finance 52 (3), 923–973.Google Scholar
Singh, R., Weninger, Q. & Doyle, M. (2006) Fisheries management with stock growth uncertainty and costly capital adjustment. J. Environ. Econ. Manage. 52 (2), 582–599.Google Scholar
Slade, M. (2001) Valuing managerial flexibility: An application of real-option theory to mining investments. J. Environ. Econ. Manage. 41 (2), 193–233.Google Scholar
Staniforth, A. & Cote, J. (1991) Semi-lagrangian integration schemes for atmospheric modelsa review. Mon. Weather Rev. 119, 2206–2223.Google Scholar
Wilmott, P. (2009) Paul Wilmott on Quantitative Finance, 2nd ed., Wiley, New Jersey.Google Scholar
Wilmott, P., Howison, S. & Derwynne, J. (1995) The Mathematics of Financial Derivatives: A Student Introduction. Cambridge University Press, Cambridge, UK.Google Scholar