IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v32y2022i3p779-824.html
   My bibliography  Save this article

A mean‐field game approach to equilibrium pricing in solar renewable energy certificate markets

Author

Listed:
  • Arvind V. Shrivats
  • Dena Firoozi
  • Sebastian Jaimungal

Abstract

Solar renewable energy certificate (SREC) markets are a market‐based system that incentivizes solar energy generation. A regulatory body overseeing load serving entities imposes a lower bound on the amount of energy each regulated firm must generate via solar means, providing them with a tradeable certificate for each MWh generated. Firms seek to navigate the market optimally by modulating their SREC generation and trading rates. As such, the SREC market can be viewed as a stochastic game, where agents interact through the SREC price. We study this stochastic game by solving the mean‐field game (MFG) limit with subpopulations of heterogeneous agents. Market participants optimize costs accounting for trading frictions, cost of generation, nonlinear noncompliance costs, and generation uncertainty. Moreover, we endogenize SREC price through market clearing. We characterize firms' optimal controls as the solution of McKean–Vlasov (MV) forward‐backward stochastic differential equations (FBSDEs) and determine the equilibrium SREC price. We establish the existence and uniqueness of a solution to this MV‐FBSDE, and prove that the MFG strategies form an ε$\epsilon$‐Nash equilibrium for the finite player game. Finally, we develop a numerical scheme for solving the MV‐FBSDEs and conduct a simulation study.

Suggested Citation

  • Arvind V. Shrivats & Dena Firoozi & Sebastian Jaimungal, 2022. "A mean‐field game approach to equilibrium pricing in solar renewable energy certificate markets," Mathematical Finance, Wiley Blackwell, vol. 32(3), pages 779-824, July.
    • Handle: RePEc:bla:mathfi:v:32:y:2022:i:3:p:779-824
    DOI: 10.1111/mafi.12345
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/mafi.12345
    Download Restriction: no
    File URL: https://libkey.io/10.1111/mafi.12345?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Coulon, Michael & Khazaei, Javad & Powell, Warren B., 2015. "SMART-SREC: A stochastic model of the New Jersey solar renewable energy certificate market," Journal of Environmental Economics and Management, Elsevier, vol. 73(C), pages 13-31.
    2. Hitzemann, Steffen & Uhrig-Homburg, Marliese, 2018. "Equilibrium Price Dynamics of Emission Permits," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 53(4), pages 1653-1678, August.
    3. Eirik Amundsen & Fridrik Baldursson & Jørgen Mortensen, 2006. "Price Volatility and Banking in Green Certificate Markets," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 35(4), pages 259-287, December.
    4. A. Bensoussan & K. Sung & S. Yam, 2013. "Linear–Quadratic Time-Inconsistent Mean Field Games," Dynamic Games and Applications, Springer, vol. 3(4), pages 537-552, December.
    5. Olivier F'eron & Peter Tankov & Laura Tinsi, 2020. "Price formation and optimal trading in intraday electricity markets," Papers 2009.04786, arXiv.org, revised Jun 2021.
    6. Arvind Shrivats & Sebastian Jaimungal, 2020. "Optimal Generation and Trading in Solar Renewable Energy Certificate (SREC) Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(1-2), pages 99-131, July.
    7. Ren� Carmona & Michael Coulon & Daniel Schwarz, 2012. "The valuation of clean spread options: linking electricity, emissions and fuels," Quantitative Finance, Taylor & Francis Journals, vol. 12(12), pages 1951-1965, December.
    8. René Aïd & Matteo Basei & Huyen Pham, 2020. "A McKean-Vlasov approach to distributed electricity generation development," Post-Print hal-03714163, HAL.
    9. Hustveit, Magne & Frogner, Jens Sveen & Fleten, Stein-Erik, 2017. "Tradable green certificates for renewable support: The role of expectations and uncertainty," Energy, Elsevier, vol. 141(C), pages 1717-1727.
    10. Javad Khazaei & Michael Coulon & Warren B. Powell, 2017. "ADAPT: A Price-Stabilizing Compliance Policy for Renewable Energy Certificates: The Case of SREC Markets," Operations Research, INFORMS, vol. 65(6), pages 1429-1445, December.
    11. Michael Ludkovski & Xuwei Yang, 2017. "Mean Field Game Approach to Production and Exploration of Exhaustible Commodities," Papers 1710.05131, arXiv.org.
    12. René Carmona & Jean-Pierre Fouque & Seyyed Mostafa Mousavi & Li-Hsien Sun, 2018. "Systemic Risk and Stochastic Games with Delay," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 366-399, November.
    13. Charles-Albert Lehalle & Charafeddine Mouzouni, 2019. "A mean field game of portfolio trading and its consequences on perceived correlations," Working Papers hal-02003143, HAL.
    14. Philippe Casgrain & Sebastian Jaimungal, 2020. "Mean‐field games with differing beliefs for algorithmic trading," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 995-1034, July.
    15. Delarue, François, 2002. "On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 209-286, June.
    16. René Aïd & Matteo Basei & Huyên Pham, 2020. "A McKean–Vlasov approach to distributed electricity generation development," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(2), pages 269-310, April.
    17. Arvind Shrivats & Sebastian Jaimungal, 2019. "Optimal Behaviour in Solar Renewable Energy Certificate (SREC) Markets," Papers 1904.06337, arXiv.org, revised Apr 2020.
    18. repec:dau:papers:123456789/2267 is not listed on IDEAS
    19. Romuald Elie & Thibaut Mastrolia & Dylan Possamaï, 2019. "A Tale of a Principal and Many, Many Agents," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 440-467, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dena Firoozi & Arvind V Shrivats & Sebastian Jaimungal, 2021. "Principal agent mean field games in REC markets," Papers 2112.11963, arXiv.org, revised Jun 2022.
    2. Arvind Shrivats & Dena Firoozi & Sebastian Jaimungal, 2020. "A Mean-Field Game Approach to Equilibrium Pricing in Solar Renewable Energy Certificate Markets," Papers 2003.04938, arXiv.org, revised Aug 2021.
    3. Steven Campbell & Yichao Chen & Arvind Shrivats & Sebastian Jaimungal, 2021. "Deep Learning for Principal-Agent Mean Field Games," Papers 2110.01127, arXiv.org.
    4. Arvind Shrivats & Sebastian Jaimungal, 2019. "Optimal Behaviour in Solar Renewable Energy Certificate (SREC) Markets," Papers 1904.06337, arXiv.org, revised Apr 2020.
    5. René Carmona & Gökçe Dayanıklı & Mathieu Laurière, 2022. "Mean Field Models to Regulate Carbon Emissions in Electricity Production," Dynamic Games and Applications, Springer, vol. 12(3), pages 897-928, September.
    6. Masaaki Fujii & Akihiko Takahashi, 2021. "Equilibrium Price Formation with a Major Player and its Mean Field Limit," CARF F-Series CARF-F-509, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    7. Masaaki Fujii & Akihiko Takahashi, 2021. "Equilibrium Price Formation with a Major Player and its Mean Field Limit," Papers 2102.10756, arXiv.org, revised Feb 2022.
    8. Olivier F'eron & Peter Tankov & Laura Tinsi, 2020. "Price formation and optimal trading in intraday electricity markets with a major player," Papers 2011.07655, arXiv.org.
    9. Masaaki Fujii & Akihiko Takahashi, 2021. "``Equilibrium Price Formation with a Major Player and its Mean Field Limit''," CIRJE F-Series CIRJE-F-1162, CIRJE, Faculty of Economics, University of Tokyo.
    10. Masaaki Fujii, 2020. "Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations," CARF F-Series CARF-F-497, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    11. Xin-gang, Zhao & Yi, Zuo & Hui, Wang & Zhen, Wang, 2022. "How can the cost and effectiveness of renewable portfolio standards be coordinated? Incentive mechanism design from the coevolution perspective," Renewable and Sustainable Energy Reviews, Elsevier, vol. 158(C).
    12. Olivier Féron & Peter Tankov & Laura Tinsi, 2020. "Price Formation and Optimal Trading in Intraday Electricity Markets with a Major Player," Risks, MDPI, vol. 8(4), pages 1-21, December.
    13. Liam Welsh & Sebastian Jaimungal, 2024. "Nash Equilibria in Greenhouse Gas Offset Credit Markets," Papers 2401.01427, arXiv.org.
    14. Hui, Wang & Xin-gang, Zhao & Ling-zhi, Ren & Fan, Lu, 2021. "An agent-based modeling approach for analyzing the influence of market participants’ strategic behavior on green certificate trading," Energy, Elsevier, vol. 218(C).
    15. Baamonde-Seoane, María A. & Carmen Calvo-Garrido, María del & Coulon, Michael & Vázquez, Carlos, 2021. "Numerical solution of a nonlinear PDE model for pricing Renewable Energy Certificates (RECs)," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    16. David Evangelista & Yuri Saporito & Yuri Thamsten, 2022. "Price formation in financial markets: a game-theoretic perspective," Papers 2202.11416, arXiv.org.
    17. Ren'e Aid & Ofelia Bonesini & Giorgia Callegaro & Luciano Campi, 2021. "A McKean-Vlasov game of commodity production, consumption and trading," Papers 2111.04391, arXiv.org.
    18. Sebastian Jaimungal, 2022. "Reinforcement learning and stochastic optimisation," Finance and Stochastics, Springer, vol. 26(1), pages 103-129, January.
    19. Hustveit, Magne & Frogner, Jens Sveen & Fleten, Stein-Erik, 2017. "Tradable green certificates for renewable support: The role of expectations and uncertainty," Energy, Elsevier, vol. 141(C), pages 1717-1727.
    20. Javad Khazaei & Michael Coulon & Warren B. Powell, 2017. "ADAPT: A Price-Stabilizing Compliance Policy for Renewable Energy Certificates: The Case of SREC Markets," Operations Research, INFORMS, vol. 65(6), pages 1429-1445, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:mathfi:v:32:y:2022:i:3:p:779-824. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.