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Robust Stochastic Stackelberg Differential Reinsurance and Investment Games for an Insurer and a Reinsurer with Delay

Author

Listed:
  • Lu Yang

    (Guangdong Polytechnic Normal University)

  • Chengke Zhang

    (Guangdong University of Technology)

  • Huainian Zhu

    (Guangdong University of Technology)

Abstract

This paper investigates the asset-liability management problem for an ordinary robust insurance system between a reinsurer and an insurer under the Heston model with delay. The reinsurer, as the leader of the Stackelberg game, can price reinsurance premium and invest its wealth in a financial market that contains a risk-free asset and a risky asset whose price process is described by the Heston model. The insurer, as the follower of the Stackelberg game, can purchase proportional reinsurance from the reinsurer and invest in the same financial market. Under the consideration of the performance-related capital inflow/outflow, the wealth processes of the insurer and reinsurer are modeled by stochastic differential delay equations (SDDEs). This paper aims to find the equilibrium strategies for the reinsurer and insurer by maximizing the expected utility of the player’s terminal wealth with delay under the worst-case scenario of the alternative measures. By using the idea of backward induction and dynamic programming approach, the explicit expressions of the robust equilibrium strategies and value functions are derived. Finally, some numerical examples and sensitivity analysis to illustrate the effects of model parameters on the robust optimal reinsurance and investment strategies are performed.

Suggested Citation

  • Lu Yang & Chengke Zhang & Huainian Zhu, 2022. "Robust Stochastic Stackelberg Differential Reinsurance and Investment Games for an Insurer and a Reinsurer with Delay," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 361-384, March.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:1:d:10.1007_s11009-021-09855-9
    DOI: 10.1007/s11009-021-09855-9
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    References listed on IDEAS

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    Cited by:

    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.
    2. Guohui Guan & Zongxia Liang & Yilun Song, 2022. "A Stackelberg reinsurance-investment game under $\alpha$-maxmin mean-variance criterion and stochastic volatility," Papers 2212.14327, arXiv.org.
    3. Qiang Zhang & Qianqian Cui, 2024. "Robust Investment and Proportional Reinsurance Strategy with Delay and Jumps in a Stochastic Stackelberg Differential Game," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-34, December.
    4. Ning Bin & Huainian Zhu & Chengke Zhang, 2023. "Stochastic Differential Games on Optimal Investment and Reinsurance Strategy with Delay Under the CEV Model," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-27, June.

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