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Time-Consistent Investment-Reinsurance Strategies for the Insurer and the Reinsurer under the Generalized Mean-Variance Criteria

Author

Listed:
  • Helu Xiao

    (School of Business, Hunan Normal University, Changsha 410081, China)

  • Tiantian Ren

    (School of Business Administration, Hunan University, Changsha 410082, China)

  • Yanfei Bai

    (School of Business Administration, Hunan University, Changsha 410082, China)

  • Zhongbao Zhou

    (School of Business Administration, Hunan University, Changsha 410082, China)

Abstract

Most of the existing literature on optimal investment-reinsurance only studies from the perspective of insurers and also treats the investment-reinsurance decision as a continuous process. However, in practice, the benefits of reinsurers cannot be ignored, nor can decision-makers engage in continuous trading. Under the discrete-time framework, we first propose a multi-period investment-reinsurance optimization problem considering the joint interests of the insurer and the reinsurer, among which their performance is measured by two generalized mean-variance criteria. We derive the time-consistent investment-reinsurance strategies for the proposed model by maximizing the weighted sum of the insurer’s and the reinsurer’s mean-variance objectives. We discuss the time-consistent investment-reinsurance strategies under two special premium principles. Finally, we provide some numerical simulations to show the impact of the intertemporal restrictions on the time-consistent investment-reinsurance strategies. These results indicate that the intertemporal restrictions will urge the insurer and the reinsurer to shrink the position invested in the risky asset; however, for the time-consistent reinsurance strategy, the impact of the intertemporal restrictions depends on who is the leader in the proposed model.

Suggested Citation

  • Helu Xiao & Tiantian Ren & Yanfei Bai & Zhongbao Zhou, 2019. "Time-Consistent Investment-Reinsurance Strategies for the Insurer and the Reinsurer under the Generalized Mean-Variance Criteria," Mathematics, MDPI, vol. 7(9), pages 1-25, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:857-:d:268040
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    References listed on IDEAS

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    1. Zilan Liu & Yijun Wang & Ya Huang & Jieming Zhou, 2022. "Optimal Time-Consistent Investment and Premium Control Strategies for Insurers with Constraint under the Heston Model," Mathematics, MDPI, vol. 10(7), pages 1-22, March.

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