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Stackelberg differential reinsurance and investment game for a dependent risk model with Ornstein–Uhlenbeck process

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  • Zhang, Yawen
  • Zhang, Caibin

Abstract

This paper considers a reinsurance and investment problem under the Stackelberg differential game. It assumes that the insurer can purchase reinsurance and the claim businesses between the insurer and the reinsurer are correlated through common shock dependence, and both of them are allowed to invest in a common risky asset whose price follows an Ornstein–Uhlenbeck process. By the stochastic control theory, explicit expressions of the optimal controls and the value functions are obtained for both of the insurer and reinsurer. We show that the optimal reinsurance strategy is a constant, which is independent of the time and risk-free interest rate. We also show that compared with the independent model, the insurer will purchase less reinsurance and the reinsurer will increase the premium price under the dependent risk model.

Suggested Citation

  • Zhang, Yawen & Zhang, Caibin, 2024. "Stackelberg differential reinsurance and investment game for a dependent risk model with Ornstein–Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 214(C).
    • Handle: RePEc:eee:stapro:v:214:y:2024:i:c:s0167715224001925
    DOI: 10.1016/j.spl.2024.110223
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    References listed on IDEAS

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    1. Cao, Jingyi & Li, Dongchen & Young, Virginia R. & Zou, Bin, 2022. "Stackelberg differential game for insurance under model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 128-145.
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    6. 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.
    7. 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.
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