Quantification of uncertainty in mining project related to metal price using mean reversion process and interval type-2 fuzzy sets theory
Kvantifikacija neodređenosti cene metala u rudarskom projektu primenom procesa povratka na srednju vrednost i teorije intervalno rasplinutih skupova drugog tipa
Keywords:
mining project; uncertainty; metal price; mean reversion process simulation; interval type-2 fuzzy sets
Abstract
Real world mine project value estimation is ill defined, i.e., its parameters are not precisely known. Estimating future mineral prices - particularly prices far enough into the future to be of use in mine investment analysis - is an exercise for which a high error of estimation invariably exists. The characteristically long preproduction periods of mining projects mean that success of these capital-intensive ventures will be determined by mineral prices five to ten years in the future. The market risks related to metal price are modeled with a special stochastic process, a Mean reversion process. Validity of the parameters of the Mean reversion process directly depends on source of information. Parameters of the Mean reversion process are defined as follows: the speed of mean reversion k is fixed, the long-run equilibrium metal price P is fixed, volatility a is defined by lower and upper bound and its variation in this interval is uniform and constant over time. To decrease uncertainty we firstly make simulation of future states of metal price and after that simulated values are converted to interval type-2 fuzzy triangular numbers.References
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ZADEH, L.A. (1975) The concept of a linguistic variable and its application to reasoning. Information Science, 8 (3), pp.199-249
BELLMAN, R.E. and ZADEH, L.A. (1977) Local and fuzzy logics. In: Dunn JM, Epstein G (eds) Modern uses of multiple-valued logic. Boston: Kluwer, pp.105-151, 158-165.
BERNARD, J.T. et al. (2005) Forecastng Aluminium Prices: GARCH, Jumps and Mean-Reversion. Institut de Finance Mathematique de Montreal, October 24, pp.1-15.
DINAGAR, D.S. and ANBALAGAN, A. (2011) Two-Phase Approach For Solving Type-2 Fuzzy Linear Programming Problem. International Journal of Pure and Applied Mathematics, 70 (6), pp.873-888.
DIXIT, A.K. and PINDYCK, R.S. (1994) Investment under Uncertainty. Princeton, N.J.: Princeton University Press DO, J. et al. (2005) Comparision of Deterministic Calaculation and Fuzzy Arithmetic for Two Prediction Model Equations of Corrosion Initiation. Journal of Asian Architecture and Building Engineering, 4 (2), pp.447-454.
FERRARI, P. and SAVOIA, M. (1998) Fuzzy number theory to obtain conservative results with respect to probability. Computer methods in applied mechanics and engineering, 160, pp.205-222.
KARNIK, N.N. and MENDEL, J.M. (2001) Centroid of a type-2 fuzzy set. Information Sciences, 132, pp.195-220.
KAUFMANN, A. and GUPTA, M.M. (1985) Introduction to Fuzzy Arithmetic: Theory and Applications. New York: Van Nostrand Reinhold. KHALAF, L. et al. (2003) Simulation-Based Exact Jump Tests in Models with Conditional Heteroskedasticity. Journal of Economic Dynamic and Control, 28, pp.531-553.
LIU. F. (2008) An efficient centroid type-reduction strategy for general type-2 fuzzy logic system. Information Sciences, 178, pp.2224-2236.
MENDEL, J.M. and LIU, F. (2007) Super-Exponential Convergence of the Karnik–Mendel Algorithms for Computing the Centroid of an Interval Type-2 Fuzzy Set. IEEE Transactions on Fuzzy Systems, 15 (2), pp.309-320.
NASAB, F.G. and MALKHALIFEH, M.R. (2010) Extension of TOPSIS for Group Decision-Making Based on the Type-2 Fuzzy Positive and Negative Ideal Solutions. International Journal of Industrial Mathematics, 2 (3), pp.199-213.
SAMIS, M. (2001) Valuing a Multi-Zone Mine as a Real Asset Portfolio-A Modern Asset Pricing (Real Options) Approach. In: Proceedings of the 5thAnnual International Conference on Real Options-Theory Meets Practice. Los Angeles, California, United States, pp.1-37.
SAVOIA, M. (2002) Structural reliability analysis trough fuzzy number approach, with application to stability. Computer and Structures, 80, pp.1087-1102.
SCHWARTZ, E.S. (1997) The stochastic Behaviour of Commodity Prices: Implications for Valuation and Hedging. The Journal of Finance, 52 (3), pp.923-973.
S SCHWARTZ, E.S. and SMITH, J.E. (2000) Short-Term Variations and Long-Term Dynamics in Commodity Prices. Management Science, 46, pp.893-911.
SLADE, M.E. (2001) Valuing Managerial Flexibility: An Application of Real-Option Theory to Mining Investments. Journal of Environmental Economics and Management, 41, pp.193-233.
SWISHCHUK, A. et al. (2008) Option Pricing with Stochastic Volatility Using Fuzzy Sets Theory [Online] Northern Finance Association 2008 Conference Paper. Available from: http://www.northernfinance.org/2008/papers/182.pdf
YAO, Y.Y. (1993) Interval set algebra for qualitative knowledge representation. In: Proceedings of the 5th International Conference on Computing and Information. pp.370−375.
ZADEH, L.A. (1975) The concept of a linguistic variable and its application to reasoning. Information Science, 8 (3), pp.199-249
Published
2013-06-30
How to Cite
Gligorić, Z., Beljić, Čedomir, Gluščević, B., & Milutinović, A. (2013). Quantification of uncertainty in mining project related to metal price using mean reversion process and interval type-2 fuzzy sets theory. Podzemni Radovi, (22), 71-84. Retrieved from https://ume.rgf.bg.ac.rs/index.php/ume/article/view/62
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