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Insurance contract for electric vehicle charging stations: A Stackelberg game-theoretic approach

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  • Jin, Yuanmin
  • Jin, Zhuo
  • Wei, Jiaqin

Abstract

The development of electric vehicles has led to an expansion of Electric Vehicle Charging Stations (EVCSs). However, this expansion also brings about significant amount of risks, resulting in financial loss for EVCSs. To address this issue, this paper proposes an optimal insurance model based on a Stackelberg game between an insurer and a risk-averse EVCS operator. In the game, the insurer sets the insurance premium, and the EVCS operator decides on her charging price and ceded loss function. The paper explores the existence of the optimal solution of the game under the assumption of n-point distributed loss, and also characterizes the optimal solution if the loss follows two-point distribution. Finally, numerical examples are provided to demonstrate the effects of parameters on the optimal solution.

Suggested Citation

  • Jin, Yuanmin & Jin, Zhuo & Wei, Jiaqin, 2025. "Insurance contract for electric vehicle charging stations: A Stackelberg game-theoretic approach," Insurance: Mathematics and Economics, Elsevier, vol. 122(C), pages 61-81.
    • Handle: RePEc:eee:insuma:v:122:y:2025:i:c:p:61-81
    DOI: 10.1016/j.insmatheco.2025.02.002
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    1. Chen, Lv & Shen, Yang, 2018. "On A New Paradigm Of Optimal Reinsurance: A Stochastic Stackelberg Differential Game Between An Insurer And A Reinsurer," ASTIN Bulletin, Cambridge University Press, vol. 48(2), pages 905-960, May.
    2. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
    3. Maxime C. Cohen, & Georgia Perakis & Robert S. Pindyck, 2021. "A Simple Rule for Pricing with Limited Knowledge of Demand," Management Science, INFORMS, vol. 67(3), pages 1608-1621, March.
    4. Jinzhi Bu & David Simchi-Levi & Li Wang, 2023. "Offline Pricing and Demand Learning with Censored Data," Management Science, INFORMS, vol. 69(2), pages 885-903, February.
    5. Maxime C. Cohen & Adam N. Elmachtoub & Xiao Lei, 2022. "Price Discrimination with Fairness Constraints," Management Science, INFORMS, vol. 68(12), pages 8536-8552, December.
    6. Havrylenko, Yevhen & Hinken, Maria & Zagst, Rudi, 2024. "Risk sharing in equity-linked insurance products: Stackelberg equilibrium between an insurer and a reinsurer," ASTIN Bulletin, Cambridge University Press, vol. 54(1), pages 129-158, January.
    7. Szpiro, George G., 1988. "Insurance, risk aversion and demand for insurance," Journal of Banking & Finance, Elsevier, vol. 6(1, Supple), pages 1-125, January.
    8. Jingyi Cao & Dongchen Li & Virginia R. Young & Bin Zou, 2024. "Optimal Insurance to Maximize Exponential Utility when Premium is Computed by a Convex Functional," Papers 2401.08094, arXiv.org.
    9. Cheung, Ka Chun & Yam, Sheung Chi Phillip & Zhang, Yiying, 2019. "Risk-adjusted Bowley reinsurance under distorted probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 64-72.
    10. Knut Aase, 2009. "The Nash bargaining solution vs. equilibrium in a reinsurance syndicate," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2009(3), pages 219-238.
    11. A. Y. Golubin, 2006. "Pareto‐Optimal Insurance Policies in the Models with a Premium Based on the Actuarial Value," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(3), pages 469-487, September.
    12. Baye, Michael R & Crocker, Keith J & Ju, Jiandong, 1996. "Divisionalization, Franchising, and Divestiture Incentives in Oligopoly," American Economic Review, American Economic Association, vol. 86(1), pages 223-236, March.
    13. Jun Cai & Yichun Chi, 2020. "Optimal reinsurance designs based on risk measures: a review," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 4(1), pages 1-13, July.
    14. Boonen, Tim J. & Ghossoub, Mario, 2023. "Bowley vs. Pareto optima in reinsurance contracting," European Journal of Operational Research, Elsevier, vol. 307(1), pages 382-391.
    15. Chen, Lv & Shen, Yang, 2019. "Stochastic Stackelberg differential reinsurance games under time-inconsistent mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 120-137.
    16. Chen, Lv & Shen, Yang & Su, Jianxi, 2020. "A continuous-time theory of reinsurance chains," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 129-146.
    17. Sid Browne, 1995. "Optimal Investment Policies for a Firm With a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 937-958, November.
    18. Zuo Quan Xu & Xun Yu Zhou & Sheng Chao Zhuang, 2019. "Optimal insurance under rank‐dependent utility and incentive compatibility," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 659-692, April.
    19. Jun Cai & Yichun Chi, 2020. "Responses to discussions on ‘Optimal reinsurance designs based on risk measures: a review’," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 4(1), pages 26-27, July.
    20. Boonen, Tim J. & Tan, Ken Seng & Zhuang, Sheng Chao, 2016. "Pricing In Reinsurance Bargaining With Comonotonic Additive Utility Functions," ASTIN Bulletin, Cambridge University Press, vol. 46(2), pages 507-530, May.
    21. Florian Knobloch & Steef V. Hanssen & Aileen Lam & Hector Pollitt & Pablo Salas & Unnada Chewpreecha & Mark A. J. Huijbregts & Jean-Francois Mercure, 2020. "Net emission reductions from electric cars and heat pumps in 59 world regions over time," Nature Sustainability, Nature, vol. 3(6), pages 437-447, June.
    22. Jonathan Levin & Andrzej Skrzypacz, 2016. "Properties of the Combinatorial Clock Auction," American Economic Review, American Economic Association, vol. 106(9), pages 2528-2551, September.
    23. Cai, Jun & Liu, Haiyan & Wang, Ruodu, 2017. "Pareto-optimal reinsurance arrangements under general model settings," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 24-37.
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