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Time-Consistent Investment and Reinsurance Strategies for Mean-Variance Insurers under Stochastic Interest Rate and Stochastic Volatility

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  • Jiaqi Zhu

    (Department of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China)

  • Shenghong Li

    (Department of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China)

Abstract

This paper studies the time-consistent optimal investment and reinsurance problem for mean-variance insurers when considering both stochastic interest rate and stochastic volatility in the financial market. The insurers are allowed to transfer insurance risk by proportional reinsurance or acquiring new business, and the jump-diffusion process models the surplus process. The financial market consists of a risk-free asset, a bond, and a stock modelled by Heston’s stochastic volatility model. Interest rate in the market is modelled by the Vasicek model. By using extended dynamic programming approach, we explicitly derive equilibrium reinsurance-investment strategies and value functions. In addition, we provide and prove a verification theorem and then prove the solution we get satisfies it. Moreover, sensitive analysis is given to show the impact of several model parameters on equilibrium strategy and the efficient frontier.

Suggested Citation

  • Jiaqi Zhu & Shenghong Li, 2020. "Time-Consistent Investment and Reinsurance Strategies for Mean-Variance Insurers under Stochastic Interest Rate and Stochastic Volatility," Mathematics, MDPI, vol. 8(12), pages 1-22, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2183-:d:458124
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    References listed on IDEAS

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    Cited by:

    1. Chunwei Wang & Naidan Deng & Silian Shen, 2022. "Numerical Method for a Perturbed Risk Model with Proportional Investment," Mathematics, MDPI, vol. 11(1), pages 1-27, December.
    2. Jiaen Xu & Chunwei Wang & Naidan Deng & Shujing Wang, 2023. "Numerical Method for a Risk Model with Two-Sided Jumps and Proportional Investment," Mathematics, MDPI, vol. 11(7), pages 1-22, March.

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