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Robust investment decisions under supply disruption in petroleum markets. (English) Zbl 1307.91140
Summary: Energy-dependent economies and energy security strategies need to cope with oil and gas supply disruptions that are rare but persistent and can be financially catastrophic. This paper proposes a tractable approach for determining robust investment strategies in petroleum markets under the risk of supply disruption when asset prices follow geometric mean-reverting jump processes. The robust counterpart of the portfolio management problem under supply disruption is derived for several symmetric and asymmetric representations of the uncertainties in the problem. Computational experiments with real market data indicate that the robust optimization approach using uncertainty sets tailored to the characteristics of the data results in strategies with superior worst-case performance.

MSC:
91B74 Economic models of real-world systems (e.g., electricity markets, etc.)
90B50 Management decision making, including multiple objectives
91B38 Production theory, theory of the firm
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[1] Ben-Tal, A.; Nemirovski, A., Robust convex optimization, Mathematics of Operations Research, 23, 769-805, (1998) · Zbl 0977.90052
[2] Ben-Tal, A.; Nemirovski, A., Robust solutions of uncertain linear programs, Operation Research Letters, 25, 1-13, (1999) · Zbl 0941.90053
[3] Ben-Tal, A.; Nemirovski, A., Robust solutions of linear programming problems contaminated with uncertain data, Mathematical Programming, 88, 411-424, (2000) · Zbl 0964.90025
[4] Ben-Tal A, Nemirovski A. Lectures on modern convex optimization: analysis, algorithms, and engineering applications. MPS-SIAM Series on Optimization, Society for Industrial and Applied Mathematics, Philadelphia; 2001. · Zbl 0986.90032
[5] Ben-Tal, A.; Margelit, T.; Nemirovski, A., Robust modeling of multi-stage portfolio problems, (Frenk, H.; Roos, K.; Terlaky, T.; Zhang, S., High-performance optimization, (2002), Kluwer Academic Publishers), 303-328 · Zbl 1016.91055
[6] Bertsimas, D.; Sim, M., The price of robustness, Operations Research, 52, 35-53, (2004) · Zbl 1165.90565
[7] Bertsimas, D.; Pachamanova, D.; Sim, M., Robust linear optimization under general norms, Operations Research Letters, 32, 510-516, (2004) · Zbl 1054.90046
[8] Bertsimas, D.; Pachamanova, D., Robust multiperiod portfolio management with transaction costs, Computers and Operations Research, 35, 3-17, (2008) · Zbl 1139.91333
[9] Chen, X.; Sim, M.; Sun, P., A robust optimization perspective on stochastic programming, Operations Research, 55, 1058-1071, (2007) · Zbl 1167.90608
[10] Chen, D.; Kwon, R. H., Robust portfolio selection for index tracking, Computers and Operations Research, 39, 4, 829-837, (2012) · Zbl 1251.91053
[11] Clewlow, L.; Strickland, C., Energy derivativespricing and risk management, (2000), Lacima Group
[12] Curlee, T. R.; Turhollow, A. F.; Das, S., Oil supply disruptions and modeling methodologiesthe role of LP models, Energy Economics, 10, 147-154, (1988)
[13] Energy Information Administration: Nigeria Report 2007. URL 〈http://www.eia.doe.gov〉.
[14] El Ghaoui, L.; Lebret, H., Robust solutions to least-squares problems with uncertain data, SIAM Journal of Matrix Analysis and Applications, 18, 1035-1064, (1997) · Zbl 0891.65039
[15] Fabozzi, F. J.; Kolm, N. P.; Pachamanova, D.; Focardi, S. M., Robust portfolio optimization and management, (2007), Wiley Finance
[16] Greene, D. L.; Hopson, J. L., Running out of and into oilanalyzing global depletion and transition through 2050, (2003), Oak Ridge National Laboratory Tennessee
[17] Goldfarb, D.; Iyengar, G., Robust portfolio selection problems, Mathematics of Operations, 28, 1-38, (2003) · Zbl 1082.90082
[18] Gulpinar N, Katata K. Modelling oil and gas supply disruption risks using extreme value theory and copula. Journal of Applied Statistics, available online 6 Sept 2013.
[19] Gulpinar, N.; Rustem, B., Optimal decisions and robust methods for forecast errors, Computational Statistics and Data Analysis, 51, 3595-3611, (2007) · Zbl 1161.62422
[20] Gulpinar, N.; Rustem, B., Worst-case optimal robust decisions for multi-period portfolio optimization, European Journal of Operational Research, 183, 981-1000, (2007) · Zbl 1138.91446
[21] Hull, J., Options, futures and other derivatives, (2008), Prentice-Hall · Zbl 1087.91025
[22] Kawas, B.; Thiele, A., A log-robust optimization approach to portfolio management, OR Spectrum, 20, 1-27, (2009)
[23] Kleindorfer, P. R.; Saad, G. H., Managing disruption risks in supply chains, Production and Operations Management, 14, 53-68, (2005)
[24] Markowitz, H., Portfolio selection, Journal of Finance, 7, 77-91, (1952)
[25] Moon, Y.; Yao, T., A robust mean absolute deviation model for portfolio optimization, Computers and Operations Research, 38, 9, 1251-1258, (2011) · Zbl 1208.91137
[26] McCann, K.; Nordström, M., Product summary, energy derivatives, (1995), Financial Markets Unit Federal Reserve Bank of Chicago
[27] Natarajan, K.; Pachamanova, D.; Sim, M., Incorporating asymmetric distributional information in robust value-at-risk optimization, Management Science, 54, 573-585, (2008) · Zbl 1142.91593
[28] Natarajan, K.; Pachamanova, D.; Sim, M., Constructing risk measures from uncertainty sets, Operations Research, 57, 5, 1129-1141, (2009) · Zbl 1233.91153
[29] Pachamanova, D.; Fabozzi, F., Simulation and optimization in financemodeling with MATLAB. @RISK, or VBA, (2010), John Wiley & Sons Hoboken, NJ · Zbl 1217.91002
[30] Pachamanova, D., Handling parameter uncertainty in portfolio risk minimizationthe robust optimization approach, Journal of Portfolio Management, 32, 70-78, (2006)
[31] Pilipovic, D., Energy riskvaluing and managing energy derivatives, (2007), McGraw-Hill
[32] Reister, D. B., A compact model of oil supply disruptions, Resources and Energy, 10, 161-183, (1988)
[33] Schwartz, E. S., The stochastic behavior of commodity prices: implications for valuation and hedging, Journal of Finance, 52, 923-973, (1997)
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