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Multistage stochastic portfolio optimisation in deregulated electricity markets using linear decision rules

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  • Rocha, Paula
  • Kuhn, Daniel

Abstract

The deregulation of electricity markets increases the financial risk faced by retailers who procure electric energy on the spot market to meet their customers’ electricity demand. To hedge against this exposure, retailers often hold a portfolio of electricity derivative contracts. In this paper, we propose a multistage stochastic mean–variance optimisation model for the management of such a portfolio. To reduce computational complexity, we apply two approximations: we aggregate the decision stages and solve the resulting problem in linear decision rules (LDR). The LDR approach consists of restricting the set of recourse decisions to those affine in the history of the random parameters. When applied to mean–variance optimisation models, it leads to convex quadratic programs. Since their size grows typically only polynomially with the number of periods, they can be efficiently solved. Our numerical experiments illustrate the value of adaptivity inherent in the LDR method and its potential for enabling scalability to problems with many periods.

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  • Rocha, Paula & Kuhn, Daniel, 2012. "Multistage stochastic portfolio optimisation in deregulated electricity markets using linear decision rules," European Journal of Operational Research, Elsevier, vol. 216(2), pages 397-408.
    • Handle: RePEc:eee:ejores:v:216:y:2012:i:2:p:397-408
    DOI: 10.1016/j.ejor.2011.08.001
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    1. Mount, Timothy D. & Ning, Yumei & Cai, Xiaobin, 2006. "Predicting price spikes in electricity markets using a regime-switching model with time-varying parameters," Energy Economics, Elsevier, vol. 28(1), pages 62-80, January.
    2. Deng, S.J. & Oren, S.S., 2006. "Electricity derivatives and risk management," Energy, Elsevier, vol. 31(6), pages 940-953.
    3. Alexander Shapiro, 2003. "Inference of statistical bounds for multistage stochastic programming problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(1), pages 57-68, September.
    4. Geyer, Alois & Hanke, Michael & Weissensteiner, Alex, 2010. "No-arbitrage conditions, scenario trees, and multi-asset financial optimization," European Journal of Operational Research, Elsevier, vol. 206(3), pages 609-613, November.
    5. Suvrajeet Sen & Lihua Yu & Talat Genc, 2006. "A Stochastic Programming Approach to Power Portfolio Optimization," Operations Research, INFORMS, vol. 54(1), pages 55-72, February.
    6. Alper Atamtürk & Muhong Zhang, 2007. "Two-Stage Robust Network Flow and Design Under Demand Uncertainty," Operations Research, INFORMS, vol. 55(4), pages 662-673, August.
    7. Xin Chen & Melvyn Sim & Peng Sun & Jiawei Zhang, 2008. "A Linear Decision-Based Approximation Approach to Stochastic Programming," Operations Research, INFORMS, vol. 56(2), pages 344-357, April.
    8. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    9. Aharon Ben-Tal & Boaz Golany & Arkadi Nemirovski & Jean-Philippe Vial, 2005. "Retailer-Supplier Flexible Commitments Contracts: A Robust Optimization Approach," Manufacturing & Service Operations Management, INFORMS, vol. 7(3), pages 248-271, February.
    10. Angelos Georghiou & Wolfram Wiesemann & Daniel Kuhn, 2010. "Generalized Decision Rule Approximations for Stochastic Programming via Liftings," Working Papers 043, COMISEF.
    11. Klaassen, Pieter, 1997. "Discretized reality and spurious profits in stochastic programming models for asset/liability management," Serie Research Memoranda 0011, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    12. Klaassen, Pieter, 1997. "Discretized reality and spurious profits in stochastic programming models for asset/liability management," European Journal of Operational Research, Elsevier, vol. 101(2), pages 374-392, September.
    13. Teemu Pennanen, 2005. "Epi-Convergent Discretizations of Multistage Stochastic Programs," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 245-256, February.
    14. Jitka Dupačová & Giorgio Consigli & Stein Wallace, 2000. "Scenarios for Multistage Stochastic Programs," Annals of Operations Research, Springer, vol. 100(1), pages 25-53, December.
    15. Michael S. Casey & Suvrajeet Sen, 2005. "The Scenario Generation Algorithm for Multistage Stochastic Linear Programming," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 615-631, August.
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    17. Frans J. C. T. Ruiter & Aharon Ben-Tal & Ruud C. M. Brekelmans & Dick Hertog, 2017. "Robust optimization of uncertain multistage inventory systems with inexact data in decision rules," Computational Management Science, Springer, vol. 14(1), pages 45-66, January.
    18. Xiaojia Guo & Alexandros Beskos & Afzal Siddiqui, 2016. "The natural hedge of a gas-fired power plant," Computational Management Science, Springer, vol. 13(1), pages 63-86, January.
    19. Barbara Glensk & Reinhard Madlener, 2013. "Multi-period portfolio optimization of power generation assets," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 23(4), pages 20-38.
    20. Downward, Anthony & Young, David & Zakeri, Golbon, 2016. "Electricity retail contracting under risk-aversion," European Journal of Operational Research, Elsevier, vol. 251(3), pages 846-859.
    21. Moreira, Alexandre & Pozo, David & Street, Alexandre & Sauma, Enzo & Strbac, Goran, 2021. "Climate‐aware generation and transmission expansion planning: A three‐stage robust optimization approach," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1099-1118.
    22. Charwand, Mansour & Gitizadeh, Mohsen & Siano, Pierluigi, 2017. "A new active portfolio risk management for an electricity retailer based on a drawdown risk preference," Energy, Elsevier, vol. 118(C), pages 387-398.
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    24. Debbie Dupuis, Geneviève Gauthier, and Fréderic Godin, 2016. "Short-term Hedging for an Electricity Retailer," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).

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