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Robust portfolio selection problem under temperature uncertainty. (English) Zbl 1395.91445
Summary: In this paper, we consider a portfolio selection problem under temperature uncertainty. Weather derivatives based on different temperature indices are used to protect against undesirable temperature events. We introduce stochastic and robust portfolio optimization models using weather derivatives. The investors’ different risk preferences are incorporated into the portfolio allocation problem. The robust investment decisions are derived in view of discrete and continuous sets that the underlying uncertain data in temperature model belong. We illustrate main features of the robust approach and performance of the portfolio optimization models using real market data. In particular, we analyze impact of various model parameters on different robust investment decisions.

MSC:
91G20 Derivative securities (option pricing, hedging, etc.)
91G10 Portfolio theory
90C31 Sensitivity, stability, parametric optimization
86A32 Geostatistics
Software:
QRM
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[1] Alaton, P.; Djehiche, B.; Stillberger, D., On modelling and pricing weather derivatives, Applied Mathematical Finance, 9, 1, 1-20, (2002) · Zbl 1013.91036
[2] Bacon, C. R., (2008). Practical portfolio performance measurement and attribution (2nd ed.).
[3] Bank, M.; Wiesner, R., Determinants of weather derivatives usage in the Austrian winter tourism industry, Tourism Management, 32, 1, 62-68, (2011)
[4] Barth, A.; Benth, F. E.; Potthoff, J., Hedging of spatial temperature risk with market-traded futures, Applied Mathematical Finance, 18, 2, 93-117, (2011) · Zbl 1213.91147
[5] Ben-Tal, A.; Nemirovski, A.; Roos, C., Robust solutions of uncertain quadratic and conic-quadratic problems, SIAM Journal on Optimization, 13, 2, 535–560, (2002) · Zbl 1026.90065
[6] Ben-Tal, A.; Ghaoui, L. E.; Nemirovski, A., Robust optimization, (2009), Princeton University Press
[7] Ben-Tal, A.; Nemirovski, A., Robust convex optimization, Mathematics of Operations Research, 23, 4, 769-805, (1998) · Zbl 0977.90052
[8] Benth, F. E.; Saltyte-Benth, J., Stochastic modelling of temperature variations with a view towards weather derivatives, Applied Mathematical Finance, 12, 53-85, (2005) · Zbl 1093.91021
[9] Benth, F. E.; Saltyte-Benth, J., The volatility of temperature and pricing of weather derivatives, Quantitative Finance, 7, 5, 553-561, (2007) · Zbl 1151.91481
[10] Benth, F. E.; Saltyte-Benth, J., Weather derivatives and stochastic modelling of temperature, InternationalJournal of Stochastic Analysis, 2011, 1-21, (2011), Article ID 576791 · Zbl 1229.91298
[11] Benth, F. E.; Saltyte-Benth, J.; Koekebakker, S., Stochastic modelling of electricity and related markets, (2008), World Scientific · Zbl 1143.91002
[12] Bertrand, J.; Brusset, X.; Fortin, M., Assessing and hedging the cost of unseasonal weather: case of the apparel sector, European Journal of Operational Research, 244, 1, 261-276, (2015) · Zbl 1346.91260
[13] Bertsimas, D.; Pachamanova, D., Robust multiperiod portfolio management in the presence of transaction costs, Computers & Operations Research, 35, 1, 3-17, (2008) · Zbl 1139.91333
[14] Bertsimas, D.; Gupta, V.; Kallus, N., Data-driven robust optimization, Operations Research, (2013)
[15] Bertsimas, D.; Pachamanova, D.; Sim, M., Robust linear optimization under general norms, OR Letters, 32, 510-516, (2004) · Zbl 1054.90046
[16] Brockett, P. L.; Wang, M.; Yang, C., Weather derivatives and weather risk management, Risk Management and Insurance Review, 8, 1, 127-140, (2005)
[17] Brockett, P. L.; Wang, M.; Yang, C. C.; Zou, H., Portfolio effects and valuation of weather derivatives, Financial Review, 41, 1, 55-76, (2006)
[18] Brody, D. C.; Syroka, J.; Zervos, M., Dynamical pricing of weather derivatives, Quantitative Finance, 2, 3, 189-198, (2002)
[19] Cao, M.; Li, A.; Wei, J., Watching the weather report, Canadian Investment Review, Summer, 27-33, (2004)
[20] Cao, M.; Wei, J., Weather derivatives valuation and market price of weather risk, Journal of Futures Markets, 24, 11, 1065-1089, (2004)
[21] Ceria, S.; Stubbs, R., Incorporating estimation errors into portfolio selection: robust portfolio construction, Journal of Asset Management, 7, 2, 109-127, (2006)
[22] Chaffin, W. W.; Rhiel, S. G., The effect of skewness and kurtosis on the one-sample T test and the impact of knowledge of the population standard deviation, Journal of Statistical Computation and Simulation, 46, 1-2, 79-90, (1993)
[23] Chen, X.; Sim, M.; Sun, P., A robust optimization perspective on stochastic programming, Operations Research, 55, 6, 1058-1071, (2007) · Zbl 1167.90608
[24] Dorfleitner, G.; Wimmer, M., The pricing of temperature futures at the Chicago mercantile exchange, Journal of Banking and Finance, 34, 6, 1360-1370, (2010)
[25] El Ghaoui, L.; Lebret, H., Robust solutions to least-squares problems with uncertain data, SIAM Journal Matrix Analysis and Applications, 18, 4, 1035-1064, (1997) · Zbl 0891.65039
[26] Elias, R. S.; Wahab, M. I.M.; Fang, L., A comparison of regime-switching temperature modeling approaches for applications in weather derivatives, European Journal of Operational Research, 232, 3, 549-560, (2014) · Zbl 1305.91228
[27] Ellithorpe, G.; Punman, S., Weather derivatives and their implications for power markets, The Journal of Risk Finance, 1, 2, 19-28, (2000)
[28] Fabozzi, F.; Kolm, P.; Pachamanova, D.; Focardi, S., Robust portfolio optimization & management, (2007), Wiley & Sons
[29] Garman, M.; Blanco, C.; Erickson, R., Weather derivatives: instruments and pricing issues, (2000), Financial Engineering Associates
[30] Goldfarb, D.; Iyengar, G., Robust portfolio selection problem, Mathematics of Operations Research, 28, 1, 1-37, (2003) · Zbl 1082.90082
[31] Gorissen, B. L.; Yanikoglu, I.; Den Hertog, D., Hints for practical robust optimization, 2013-065, (2013), CentER
[32] Gulpinar, N.; Rustem, B., Optimal decisions and robust methods for forecast errors, Computational Statistics and Data Analysis, 51, 3595-3611, (2007) · Zbl 1161.62422
[33] Gülpınar, N.; Katata, K.; Pachamanova, D., Robust portfolio allocation under discrete asset choice constraints, Journal of Asset Management, 12, 1, 67-83, (2011)
[34] Hamisultane, H., Utility-based pricing of weather derivatives, The European Journal of Finance, 16, 6, 503-525, (2010)
[35] Hardle, K. W.; Lopez-Cabrera, B.; Ritter, M., Forecast based pricing of weather derivatives, (2012)
[36] Jewson, S. (2002). Weather derivative pricing and risk management: volatility and value at risk.
[37] Jewson, S., Weather derivative pricing and the potential accuracy of daily temperature modelling, Risk management solutions, (2004), London, UK
[38] Jewson, S.; Brix, A., Weather derivative valuation: The meteorological, statistical, financial and mathematical foundations, (2005), Cambridge University Press
[39] Kawas, B.; Thiele, A., A log Â-robust optimization approach to portfolio management, (2009), OR Spectrum
[40] Lofberg, J., Yalmipa toolbox for modeling and optimization in MATLAB, Proceedings of CACSD conference, Taiwan, (2004)
[41] McNeil, A. J.; Frey, R.; Embrechts, P., Quantitative risk management: Concepts, techniques and tools, (2005), Princeton University Press · Zbl 1089.91037
[42] Moon, Y.; Yao, T., A simple robust mean absolute deviation model for portfolio optimization, Computers and Operational Research, 38, 9, 1251-1258, (2011) · Zbl 1208.91137
[43] Musshoff, O.; Hirschauer, N.; Odening, M., Portfolio effects and the willingness to pay for weather insurances, Agricultural Finance Review, 68, 1, 83-97, (2008)
[44] Natarajan, K.; Pachamanova, D.; Sim, M., Incorporating asymmetric distributional information in robust value-at-risk optimization, Management Science, 54, 3, 573-585, (2008) · Zbl 1142.91593
[45] Oguzsoy, C. B.; Güven, S., Robust portfolio planning in the presence of market anomalies, Omega, 35, 1, 1-6, (2007)
[46] Rockafellar, R. T.; Uryasev, S., Optimization of conditional value-at-risk, The Journal of Risk, 2, 3, 21-41, (2000)
[47] Saltyte-Benth, J.; Benth, F. E., A critical view on temperature modelling for application in weather derivatives markets, Energy Economics, 34, 592-602, (2012)
[48] Schiller, F.; Seidler, G.; Wimmer, M., Temperature models for pricing weather derivatives, Quantitative Finance, 12, 3, 489-500, (2012) · Zbl 1278.91168
[49] Soyster, A. L.; Murphy, F. H., A unifying framework for duality and modeling in robust linear programs, Omega, 41, 6, 984-997, (2013)
[50] Svec, J.; Stevenson, M., Modelling and forecasting temperature based weather derivatives, Global Finance Journal, 18, 2, 185-204, (2007)
[51] The Economist Magazine (2012). Weather derivatives: Come rain or shine. http://www.economist.com/node/21546019.
[52] Turvey, C. G., Weather derivatives for specific event risks in agriculture, Review of Agricultural Economics, 23, 2, 333-351, (2001)
[53] Woodard, J. D.; Garcia, P., Weather derivatives, spatial aggregation, and systemic risk: implications for reinsurance hedging, Journal of Agricultural and Resource Economics, 33, 1, 34-51, (2008)
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