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Optimal mean–variance investment/reinsurance with common shock in a regime-switching market

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  • Junna Bi

    (East China Normal University)

  • Zhibin Liang

    (Nanjing Normal University)

  • Kam Chuen Yuen

    (The University of Hong Kong)

Abstract

In this paper, we consider the problem of optimal investment-reinsurance with two dependent classes of insurance risks in a regime-switching financial market. In our model, the two claim-number processes are correlated through a common shock component, and the market mode is classified into a finite number of regimes. We also assume that the insurer can purchase proportional reinsurance and invest its surplus in a financial market, and that the values of the model parameters depend on the market mode. Using the techniques of stochastic linear-quadratic control, under the mean–variance criterion, we obtain analytic expressions for the optimal investment and reinsurance strategies, and derive closed-form expressions for the efficient strategies and the efficient frontiers which are based on the solutions to some systems of linear ordinary differential equations. Finally, we carry out a numerical study for illustration purpose.

Suggested Citation

  • Junna Bi & Zhibin Liang & Kam Chuen Yuen, 2019. "Optimal mean–variance investment/reinsurance with common shock in a regime-switching market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(1), pages 109-135, August.
    • Handle: RePEc:spr:mathme:v:90:y:2019:i:1:d:10.1007_s00186-018-00657-3
    DOI: 10.1007/s00186-018-00657-3
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    References listed on IDEAS

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    Cited by:

    1. Yingxu Tian & Zhongyang Sun & Junyi Guo, 2022. "Optimal Mean-Variance Investment-Reinsurance Strategy for a Dependent Risk Model with Ornstein-Uhlenbeck Process," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1169-1191, June.
    2. Claudia Ceci & Katia Colaneri & Alessandra Cretarola, 2021. "Optimal Reinsurance and Investment under Common Shock Dependence Between Financial and Actuarial Markets," Papers 2105.07524, arXiv.org.

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