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Stochastic differential reinsurance game for two competitive insurers with ambiguity-aversion under mean-variance premium principle

Author

Listed:
  • Yu Yuan

    (Nanjing University of Information Science and Technology)

  • Kexin Wang

    (Nanjing University of Information Science and Technology)

  • Caibin Zhang

    (Nanjing University of Finance and Economics)

Abstract

In this paper, we design a competition framework for two insurers with ambiguity aversion under the utility framework and investigate the resulting stochastic reinsurance game problem. Each insurer does not have perfect confidence in the drift terms of the insurance risk and chooses to purchase per-loss reinsurance to reduce her claim risk, and the reinsurance premium is determined via the mean-variance premium principle. The objective of each insurer is to find the optimal reinsurance strategy so as to maximize the ratio of expected utility of her terminal payoff to her competitor’s under the worst-case scenario. By the dynamic programming principle and corresponding Hamilton–Jacobi–Bellman–Isaacs equation, we derive the solutions for both the equilibrium reinsurance strategy and value function under the exponential utility function. In particular, we examine the existence and uniqueness of equilibrium strategy. Finally, several numerical examples are presented to illustrate the effects of competitive relationship, ambiguity aversion and some important model parameters on the equilibrium strategy, which provide useful insights for reinsurance in reality.

Suggested Citation

  • Yu Yuan & Kexin Wang & Caibin Zhang, 2024. "Stochastic differential reinsurance game for two competitive insurers with ambiguity-aversion under mean-variance premium principle," Annals of Operations Research, Springer, vol. 335(1), pages 441-467, April.
    • Handle: RePEc:spr:annopr:v:335:y:2024:i:1:d:10.1007_s10479-024-05844-6
    DOI: 10.1007/s10479-024-05844-6
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    References listed on IDEAS

    as
    1. Matteo Brachetta & Claudia Ceci, 2019. "A BSDE-based approach for the optimal reinsurance problem under partial information," Papers 1910.05999, arXiv.org, revised May 2020.
    2. Yuen, Kam Chuen & Liang, Zhibin & Zhou, Ming, 2015. "Optimal proportional reinsurance with common shock dependence," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 1-13.
    3. Suleyman Basak & Dmitry Makarov, 2014. "Strategic Asset Allocation in Money Management," Journal of Finance, American Finance Association, vol. 69(1), pages 179-217, February.
    4. Chen, Lv & Qian, Linyi & Shen, Yang & Wang, Wei, 2016. "Constrained investment–reinsurance optimization with regime switching under variance premium principle," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 253-267.
    5. Li, Peng & Zhou, Ming & Yin, Chuancun, 2015. "Optimal reinsurance with both proportional and fixed costs," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 134-141.
    6. Baltas, I. & Dopierala, L. & Kolodziejczyk, K. & Szczepański, M. & Weber, G.-W. & Yannacopoulos, A.N., 2022. "Optimal management of defined contribution pension funds under the effect of inflation, mortality and uncertainty," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1162-1174.
    7. Junna Bi & Jun Cai & Yan Zeng, 2021. "Equilibrium reinsurance-investment strategies with partial information and common shock dependence," Annals of Operations Research, Springer, vol. 307(1), pages 1-24, December.
    8. 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.
    9. E. Savku & G.-W Weber, 2022. "Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market," Annals of Operations Research, Springer, vol. 312(2), pages 1171-1196, May.
    10. Bai, Lihua & Cai, Jun & Zhou, Ming, 2013. "Optimal reinsurance policies for an insurer with a bivariate reserve risk process in a dynamic setting," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 664-670.
    11. Zhang, Xin & Meng, Hui & Zeng, Yan, 2016. "Optimal investment and reinsurance strategies for insurers with generalized mean–variance premium principle and no-short selling," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 125-132.
    12. Lars Peter Hansen & Thomas J Sargent, 2014. "A Quartet of Semigroups for Model Specification, Robustness, Prices of Risk, and Model Detection," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 4, pages 83-143, World Scientific Publishing Co. Pte. Ltd..
    13. S. David Promislow & Virginia Young, 2005. "Minimizing the Probability of Ruin When Claims Follow Brownian Motion with Drift," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(3), pages 110-128.
    14. Borch, Karl, 1960. "Reciprocal Reinsurance Treaties," ASTIN Bulletin, Cambridge University Press, vol. 1(4), pages 170-191, December.
    15. Monique Jeanblanc & Thibaut Mastrolia & Dylan Possamaï & Anthony Réveillac, 2015. "Utility Maximization With Random Horizon: A Bsde Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-43, November.
    16. O. Palancı & S. Alparslan Gök & G. Weber, 2014. "Cooperative games under bubbly uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(2), pages 129-137, October.
    17. Yu Yuan & Zhibin Liang & Xia Han, 2022. "Robust reinsurance contract with asymmetric information in a stochastic Stackelberg differential game," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2022(4), pages 328-355, April.
    18. Zheng, Xiaoxiao & Zhou, Jieming & Sun, Zhongyang, 2016. "Robust optimal portfolio and proportional reinsurance for an insurer under a CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 77-87.
    19. Güray Kara & Ayşe Özmen & Gerhard-Wilhelm Weber, 2019. "Stability advances in robust portfolio optimization under parallelepiped uncertainty," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(1), pages 241-261, March.
    20. Betül Kalaycı & Ayşe Özmen & Gerhard-Wilhelm Weber, 2020. "Mutual relevance of investor sentiment and finance by modeling coupled stochastic systems with MARS," Annals of Operations Research, Springer, vol. 295(1), pages 183-206, December.
    21. Yuan, Yu & Han, Xia & Liang, Zhibin & Yuen, Kam Chuen, 2023. "Optimal reinsurance-investment strategy with thinning dependence and delay factors under mean-variance framework," European Journal of Operational Research, Elsevier, vol. 311(2), pages 581-595.
    22. Xia Han & Zhibin Liang & Virginia R. Young, 2020. "Optimal reinsurance to minimize the probability of drawdown under the mean-variance premium principle," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(10), pages 879-903, November.
    23. Yan, Ming & Peng, Fanyi & Zhang, Shuhua, 2017. "A reinsurance and investment game between two insurance companies with the different opinions about some extra information," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 58-70.
    24. Danping Li & Yan Zeng & Hailiang Yang, 2018. "Robust optimal excess-of-loss reinsurance and investment strategy for an insurer in a model with jumps," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2018(2), pages 145-171, February.
    25. Yang, Hailiang & Zhang, Lihong, 2005. "Optimal investment for insurer with jump-diffusion risk process," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 615-634, December.
    26. Chen, Zhiping & Yang, Peng, 2020. "Robust optimal reinsurance–investment strategy with price jumps and correlated claims," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 27-46.
    27. Chi Chung Siu & Sheung Chi Phillip Yam & Hailiang Yang & Hui Zhao, 2017. "A class of nonzero-sum investment and reinsurance games subject to systematic risks," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2017(8), pages 670-707, September.
    28. Lihua Bai & Junyi Guo & Huayue Zhang, 2010. "Optimal excess-of-loss reinsurance and dividend payments with both transaction costs and taxes," Quantitative Finance, Taylor & Francis Journals, vol. 10(10), pages 1163-1172.
    29. Bai, Yanfei & Zhou, Zhongbao & Xiao, Helu & Gao, Rui & Zhong, Feimin, 2022. "A hybrid stochastic differential reinsurance and investment game with bounded memory," European Journal of Operational Research, Elsevier, vol. 296(2), pages 717-737.
    30. Brachetta, M. & Ceci, C., 2020. "A BSDE-based approach for the optimal reinsurance problem under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 1-16.
    31. Guan, Guohui & Liang, Zongxia, 2019. "Robust optimal reinsurance and investment strategies for an AAI with multiple risks," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 63-78.
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