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Optimal Portfolio in Intraday Electricity Markets Modelled by L\'evy-Ornstein-Uhlenbeck Processes

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  • Marco Piccirilli
  • Tiziano Vargiolu

Abstract

We study an optimal portfolio problem designed for an agent operating in intraday electricity markets. The investor is allowed to trade in a single risky asset modelling the continuously traded power and aims to maximize the expected terminal utility of his wealth. We assume a mean-reverting additive process to drive the power prices. In the case of logarithmic utility, we reduce the fully non-linear Hamilton-Jacobi-Bellman equation to a linear parabolic integro-differential equation, for which we explicitly exhibit a classical solution in two cases of modelling interest. The optimal strategy is given implicitly as the solution of an integral equation, which is possible to solve numerically as well as to describe analytically. An analysis of two different approximations for the optimal policy is provided. Finally, we perform a numerical test by adapting the parameters of a popular electricity spot price model.

Suggested Citation

  • Marco Piccirilli & Tiziano Vargiolu, 2018. "Optimal Portfolio in Intraday Electricity Markets Modelled by L\'evy-Ornstein-Uhlenbeck Processes," Papers 1807.01979, arXiv.org.
    • Handle: RePEc:arx:papers:1807.01979
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    References listed on IDEAS

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    1. Arthur Henriot, 2014. "Market Design with Centralized Wind Power Management: Handling Low-predictability in Intraday Markets," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1).
    2. Thaleia Zariphopoulou, 1999. "Optimal investment and consumption models with non-linear stock dynamics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 271-296, October.
    3. Laura Pasin & Tiziano Vargiolu, 2010. "Optimal Portfolio for CRRA Utility Functions when Risky Assets are Exponential Additive Processes," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 39(1‐2), pages 65-90, February.
    4. Benth, Fred Espen & Kiesel, Rüdiger & Nazarova, Anna, 2012. "A critical empirical study of three electricity spot price models," Energy Economics, Elsevier, vol. 34(5), pages 1589-1616.
    5. Alvaro Cartea & Marcelo Figueroa, 2005. "Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 313-335.
    6. Fred Espen Benth & Kenneth Hvistendahl Karlsen & Kristin Reikvam, 2003. "Merton's portfolio optimization problem in a Black and Scholes market with non‐Gaussian stochastic volatility of Ornstein‐Uhlenbeck type," Mathematical Finance, Wiley Blackwell, vol. 13(2), pages 215-244, April.
    7. Goll, Thomas & Kallsen, Jan, 2000. "Optimal portfolios for logarithmic utility," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 31-48, September.
    8. Marius Ascheberg & Nicole Branger & Holger Kraft & Frank Thomas Seifried, 2016. "When do jumps matter for portfolio optimization?," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1297-1311, August.
    9. Rama Cont & Ekaterina Voltchkova, 2005. "Integro-differential equations for option prices in exponential Lévy models," Finance and Stochastics, Springer, vol. 9(3), pages 299-325, July.
    10. Jan Kallsen, 2000. "Optimal portfolios for exponential Lévy processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(3), pages 357-374, August.
    11. René Aïd & P. Gruet & H. Pham, 2016. "An optimal trading problem in intraday electricity markets," Post-Print hal-01609481, HAL.
    12. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    13. Helyette Geman & A. Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," Post-Print halshs-00144198, HAL.
    14. repec:dau:papers:123456789/1433 is not listed on IDEAS
    15. Latini, Luca & Piccirilli, Marco & Vargiolu, Tiziano, 2019. "Mean-reverting no-arbitrage additive models for forward curves in energy markets," Energy Economics, Elsevier, vol. 79(C), pages 157-170.
    16. {L}ukasz Delong & Claudia Kluppelberg, 2008. "Optimal investment and consumption in a Black--Scholes market with L\'evy-driven stochastic coefficients," Papers 0806.2570, arXiv.org.
    17. Garnier, Ernesto & Madlener, Reinhard, 2014. "Balancing Forecast Errors in Continuous-Trade Intraday Markets," FCN Working Papers 2/2014, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).
    18. Hélyette Geman & Andrea Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1225-1262, May.
    19. repec:bla:ecnote:v:39:y:2010:i:s1:p:65-90 is not listed on IDEAS
    20. Kiesel, Rüdiger & Paraschiv, Florentina, 2017. "Econometric analysis of 15-minute intraday electricity prices," Energy Economics, Elsevier, vol. 64(C), pages 77-90.
    21. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    22. Fred Espen Benth & Jan Kallsen & Thilo Meyer-Brandis, 2007. "A Non-Gaussian Ornstein-Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(2), pages 153-169.
    23. Fred Espen Benth & Marco Piccirilli & Tiziano Vargiolu, 2017. "Additive energy forward curves in a Heath-Jarrow-Morton framework," Papers 1709.03310, arXiv.org, revised Jun 2018.
    24. Simone Farinelli & Luisa Tibiletti, 2015. "Hydroassets Portfolio Management for Intraday Electricity Trading from a Discrete Time Stochastic Optimization Perspective," Papers 1508.05837, arXiv.org, revised Aug 2017.
    25. Aase, Knut Kristian, 1984. "Optimum portfolio diversification in a general continuous-time model," Stochastic Processes and their Applications, Elsevier, vol. 18(1), pages 81-98, September.
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