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

Author

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  • 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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Michael Ludkovski & Xuwei Yang, 2017. "Mean Field Game Approach to Production and Exploration of Exhaustible Commodities," Papers 1710.05131, arXiv.org.
    8. 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.
    9. 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.
    10. 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.
    11. Charles-Albert Lehalle & Charafeddine Mouzouni, 2019. "A mean field game of portfolio trading and its consequences on perceived correlations," Working Papers hal-02003143, HAL.
    12. 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.
    13. René Aïd & Matteo Basei & Huyen Pham, 2020. "A McKean-Vlasov approach to distributed electricity generation development," Post-Print hal-03714163, HAL.
    14. 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.
    15. 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.
    16. Arvind Shrivats & Sebastian Jaimungal, 2019. "Optimal Behaviour in Solar Renewable Energy Certificate (SREC) Markets," Papers 1904.06337, arXiv.org, revised Apr 2020.
    17. repec:dau:papers:123456789/2267 is not listed on IDEAS
    18. 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.
    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.
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