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Distributionally robust optimization with multiple time scales: valuation of a thermal power plant. (English) Zbl 07304214

Comput. Manag. Sci. 17, No. 3, 357-385 (2020); correction ibid. 17, No. 3, 387 (2020).
Summary: The valuation of a real option is preferably done with the inclusion of uncertainties in the model, since the value depends on future costs and revenues, which are not perfectly known today. The usual value of the option is defined as the maximal expected (discounted) profit one may achieve under optimal management of the operation. However, also this approach has its limitations, since quite often the models for costs and revenues are subject to model error. Under a prudent valuation, the possible model error should be incorporated into the calculation. In this paper, we consider the valuation of a power plant under ambiguity of probability models for costs and revenues. The valuation is done by stochastic dynamic programming and on top of it, we use a dynamic ambiguity model for obtaining the prudent minimax valuation. For the valuation of the power plant under model ambiguity we introduce a distance based on the Wasserstein distance. Another highlight of this paper is the multiscale approach, since decision stages are defined on a weekly basis, while the random costs and revenues appear on a much finer scale. The idea of bridging stochastic processes is used to link the weekly decision scale with the finer simulation scale. The applicability of the introduced concepts is broad and not limited to the motivating valuation problem.

MSC:

90Bxx Operations research and management science

Software:

CORO
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References:

[1] Aasgård, EK; Andersen, GS; Fleten, S.; Haugstvedt, D., Evaluating a stochastic-programming-based bidding model for a multireservoir system, IEEE Trans Power Syst, 29, 4, 1748-1757 (2014) · doi:10.1109/TPWRS.2014.2298311
[2] Bally, V.; Pagès, G., A quantization algorithm for solving multidimensional discrete-time optimal stopping problems, Bernoulli, 9, 6, 1003-1049 (2003) · Zbl 1042.60021 · doi:10.3150/bj/1072215199
[3] Bolley, F.; Guillin, A.; Villani, C., Quantitative concentration inequalities for empirical measures on non-compact spaces, Probab Theory Relat Fields, 137, 3-4, 541-593 (2007) · Zbl 1113.60093
[4] Cervellera, C.; Chen, V.; Wen, A., Optimization of a large-scale water reservoir network by stochastic dynamic programming with efficient state space discretization, Eur J Oper Res, 171, 3, 1139-1151 (2006) · Zbl 1116.90123 · doi:10.1016/j.ejor.2005.01.022
[5] Clelow, L.; Strickland, C., Energy derivatives: pricing and risk management (2000), London: Lacima Group, London
[6] Duan, C.; Fang, W.; Jiang, L.; Yao, L.; Liu, J., Distributionally robust chance-constrained approximate AC-OPF with Wasserstein metric, IEEE Trans Power Syst, 33, 5, 4924-4936 (2018) · doi:10.1109/TPWRS.2018.2807623
[7] Escudero, LF; de la Fuente, JL; Garcia, C.; Prieto, FJ, Hydropower generation management under uncertainty via scenario analysis and parallel computation, IEEE Trans Power Syst, 11, 2, 683-689 (1996) · doi:10.1109/59.496139
[8] Escudero, LF; Quintana, FJ; Salmeron, J., CORO, a modeling and an algorithmic framework for oil supply, transformation and distribution optimization under uncertainty, Eur J Oper Res, 114, 3, 638-656 (1999) · Zbl 0938.90019 · doi:10.1016/S0377-2217(98)00261-6
[9] Esfahani, PM; Kuhn, D., Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations, Math Program, 171, 1-2, 115-166 (2018) · Zbl 1433.90095 · doi:10.1007/s10107-017-1172-1
[10] Ewald, C-O; Zhang, A.; Zong, Z., On the calibration of the Schwartz two-factor model to WTI crude oil options and the extended Kalman filter, Ann Oper Res, 282, 1-2, 119-130 (2018) · Zbl 1430.91109
[11] Farkas, W.; Gourier, E.; Huitema, R.; Necula, C., A two-factor cointegrated commodity price model with an application to spread option pricing, J Bank Financ, 77, C, 249-268 (2017) · doi:10.1016/j.jbankfin.2017.01.007
[12] Fleten S-E, Haugstvedt D, Steinsbø JA, Belsnes M, Fleischmann F (2011) Bidding hydropower generation: Integrating short- and long-term scheduling. MPRA Paper 44450, University Library of Munich, Germany
[13] Fournier, N.; Guillin, A., On the rate of convergence in Wasserstein distance of the empirical measure, Probab Theory Relat Fields, 162, 3-4, 707 (2015) · Zbl 1325.60042 · doi:10.1007/s00440-014-0583-7
[14] Frangioni, A.; Gentile, C., Solving non-linear single-unit commitment problems with ramping constraints, Oper Res, 54, 4, 767-775 (2006) · Zbl 1167.90671 · doi:10.1287/opre.1060.0309
[15] Frangioni, A.; Gentile, C.; Lacalandra, F., Solving unit commitment problems with general ramp contraints, Int J Electr Power Energy Syst, 30, 316-326 (2008) · doi:10.1016/j.ijepes.2007.10.003
[16] Gao R, Kleywegt AJ (2016) Distributionally robust stochastic optimization with Wasserstein distance. arXiv preprintarXiv:1604.02199
[17] Glanzer M, Pflug GCh (2019) Multiscale stochastic optimization: modeling aspects and scenario generation. Comput Optim Appl. 10.1007/s10589-019-00135-4 · Zbl 1432.90094
[18] Glanzer, M.; Pflug, GCh; Pichler, A., Incorporating statistical model error into the calculation of acceptability prices of contingent claims, Math Program, 174, 1, 499-524 (2019) · Zbl 1421.90095 · doi:10.1007/s10107-018-1352-7
[19] Kaut, M.; Midthun, K.; Werner, A.; Tomasgard, A.; Hellemo, L.; Fodstad, M., Multi-horizon stochastic programming, Comput Manag Sci, 11, 1, 179-193 (2014) · Zbl 1298.90008 · doi:10.1007/s10287-013-0182-6
[20] Löhndorf N, Wozabal D (2018) Gas storage valuation in incomplete markets. Optimization. http://www.optimization-online.org/DB_HTML/2017/02/5863.html
[21] Maggioni F, Allevi E, Tomasgard A (2019) Bounds in multi-horizon stochastic programs. Ann Oper Res. 10.1007/s10479-019-03244-9 · Zbl 1456.90114
[22] Martinéz MG, Diniz AL, Sagastizábal C (2008) A comparative study of two forward dynamic programming techniques for solving local thermal unit commitment problems. In: 16th PSCC Conference, Glasgow Scotland, p 1-8
[23] Moriggia V, Kopa M, Vitali S (2018) Pension fund management with hedging derivatives, stochastic dominance and nodal contamination. Omega · Zbl 1381.90063
[24] Oksendal, B., Stochastic differential equations (2000), Berlin: Springer, Berlin
[25] Pflug, GCh; Pichler, A., A distance for multistage stochastic optimization models, SIAM J Optim, 22, 1, 1-23 (2012) · Zbl 1262.90118 · doi:10.1137/110825054
[26] Pflug, GCh; Pichler, A., Multistage stochastic optimization (2014), Berlin: Springer, Berlin · Zbl 1317.90220
[27] Pflug, GCh; Wozabal, D., Ambiguity in portfolio selection, Quant Financ, 7, 4, 435-442 (2007) · Zbl 1190.91138 · doi:10.1080/14697680701455410
[28] Pflug, GCh, Version-independence and nested distributions in multistage stochastic optimization, SIAM J Optim, 20, 3, 1406-1420 (2010) · Zbl 1198.90307 · doi:10.1137/080718401
[29] Ribeiro DR, Hodges SD (2004) A two-factor model for commodity prices and futures valuation. In: EFMA 2004 Basel Meetings Paper
[30] Séguin, S.; Fleten, S-E; Côté, P.; Pichler, A.; Audet, C., Stochastic short-term hydropower planning with inflow scenario trees, Eur J Oper Res, 259, 1, 1156-1168 (2017) · Zbl 1402.90224 · doi:10.1016/j.ejor.2016.11.028
[31] Seljom, P.; Tomasgard, A., The impact of policy actions and future energy prices on the cost-optimal development of the energy system in Norway and Sweden, Energy Policy, 106, C, 85-102 (2017) · doi:10.1016/j.enpol.2017.03.011
[32] Skar C, Doorman G, Pérez-Valdés GA, Tomasgard A (2016) A multi-horizon stochastic programming model for the European power system. Censes working paper 2/2016, NTNU Trondheim. ISBN: 978-82-93198-13-0
[33] van Ackooij, W.; Lopez, I. Danti; Frangioni, A.; Lacalandra, F.; Tahanan, M., Large-scale unit commitment under uncertainty: an updated literature survey, Ann Oper Res, 271, 1, 11-85 (2018) · Zbl 1411.90214 · doi:10.1007/s10479-018-3003-z
[34] van Ackooij, W.; Henrion, R.; Möller, A.; Zorgati, R., Joint chance constrained programming for hydro reservoir management, Optim Eng, 15, 509-531 (2014) · Zbl 1364.90232
[35] Werner, AS; Pichler, A.; Midthun, KT; Hellemo, L.; Tomasgard, A., Risk measures in multi-horizon scenario trees, 177-201 (2013), New York: Springer, New York
[36] Zéphyr, L.; Lang, P.; Lamond, BF, Controlled approximation of the value function in stochastic dynamic programming for multi-reservoir systems, Comput Manag Sci, 12, 4, 539-557 (2015) · Zbl 1397.90248 · doi:10.1007/s10287-015-0242-1
[37] Zhonghua S, Egging R, Huppmann D, Tomasgard A (2015) A Multi-Stage Multi-Horizon Stochastic Equilibrium Model of Multi-Fuel Energy Markets. Censes working paper 2/2016, NTNU Trondheim. ISBN: 978-82-93198-15-4
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