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A mean field game model of green economy

Author

Listed:
  • Jingguo Zhang

    (National University of Singapore)

  • Lianhai Ren

    (National University of Singapore)

Abstract

In this paper, we introduce a Mean Field Game (MFG) model of green economy and establish a related green insurance framework for insurers. Firstly, we construct an MFG of the industrial market featuring a mix of green energy-efficient companies and traditional brown companies. Each company in the industrial market needs to decide its energy consumption and will face a trade-off between investing in the development of green technologies and financial benefits, while the energy price is related to the average energy efficiency of all companies. They will also face some environmental risks, which will be hedged by green insurance. We use the fixed-point iterative algorithm to solve a Nash equilibrium of the MFG and get the firm value dynamics for the representative green and brown companies. Then, we construct a basic model for the insurer surplus process involving the green insurance premium and reinsurance strategies. We further extend the model to account for the insurer’s investment activities in fixed-income projects and green and brown indexes in the financial market. We use the deep learning method to solve the optimal reinsurance and investment strategies for insurers.

Suggested Citation

  • Jingguo Zhang & Lianhai Ren, 2024. "A mean field game model of green economy," Digital Finance, Springer, vol. 6(4), pages 657-692, December.
    • Handle: RePEc:spr:digfin:v:6:y:2024:i:4:d:10.1007_s42521-024-00118-z
    DOI: 10.1007/s42521-024-00118-z
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    References listed on IDEAS

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    1. Leland, Hayne E, 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, vol. 49(4), pages 1213-1252, September.
    2. Rene Carmona & Jean-Pierre Fouque & Li-Hsien Sun, 2013. "Mean Field Games and Systemic Risk," Papers 1308.2172, arXiv.org.
    3. Zhang, Xin & Siu, Tak Kuen, 2009. "Optimal investment and reinsurance of an insurer with model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 81-88, August.
    4. Zeng, Yan & Li, Danping & Gu, Ailing, 2016. "Robust equilibrium reinsurance-investment strategy for a mean–variance insurer in a model with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 138-152.
    5. Zeng, Yan & Li, Zhongfei & Lai, Yongzeng, 2013. "Time-consistent investment and reinsurance strategies for mean–variance insurers with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 498-507.
    6. Guanxing Fu & Chao Zhou, 2023. "Mean field portfolio games," Finance and Stochastics, Springer, vol. 27(1), pages 189-231, January.
    7. Antonietti, Roberto & Fontini, Fulvio, 2019. "Does energy price affect energy efficiency? Cross-country panel evidence," Energy Policy, Elsevier, vol. 129(C), pages 896-906.
    8. Zhang, Dongyang & Kong, Qunxi, 2022. "Renewable energy policy, green investment, and sustainability of energy firms," Renewable Energy, Elsevier, vol. 192(C), pages 118-133.
    9. Guanxing Fu, 2023. "Mean field portfolio games with consumption," Mathematics and Financial Economics, Springer, volume 17, number 4, February.
    10. Bai, Lihua & Guo, Junyi, 2008. "Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 968-975, June.
    11. Zeng, Yan & Li, Zhongfei, 2011. "Optimal time-consistent investment and reinsurance policies for mean-variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 145-154, July.
    12. 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.
    13. Luo, Shangzhen & Taksar, Michael & Tsoi, Allanus, 2008. "On reinsurance and investment for large insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 434-444, February.
    14. Jinyan Guo & Qevan Guo & Chenchen Mou & Jingguo Zhang, 2024. "A mean field game model of staking system," Digital Finance, Springer, vol. 6(3), pages 441-462, September.
    15. Avramov, Doron & Cheng, Si & Lioui, Abraham & Tarelli, Andrea, 2022. "Sustainable investing with ESG rating uncertainty," Journal of Financial Economics, Elsevier, vol. 145(2), pages 642-664.
    16. Roxana Dumitrescu & Marcos Leutscher & Peter Tankov, 2024. "Energy transition under scenario uncertainty: a mean-field game of stopping with common noise," Mathematics and Financial Economics, Springer, volume 18, number 4, February.
    17. Michael Barnett & William Brock & Lars Peter Hansen & Harrison Hong, 2020. "Pricing Uncertainty Induced by Climate Change," The Review of Financial Studies, Society for Financial Studies, vol. 33(3), pages 1024-1066.
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    More about this item

    Keywords

    Mean field game; Green economy; Green insurance; Deep learning method;
    All these keywords.

    JEL classification:

    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • G2 - Financial Economics - - Financial Institutions and Services
    • Q4 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy
    • Q5 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics

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