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Optimal combinational quota‐share and excess‐of‐loss reinsurance policies in a dynamic setting

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  • Xin Zhang
  • Ming Zhou
  • Junyi Guo

Abstract

In this paper, we describe a large insurance company's surplus by a Brownian motion with positive drift, which is the approximation of a classical risk process. The problem of minimizing the probability of ruin by controlling the combinational quota‐share and excess‐of‐loss reinsurance strategy is considered. We show that the optimal combinational reinsurance strategy must be the pure excess‐of‐loss reinsurance strategy. Moreover, we give an explicit solution for the optimal reinsurance strategy. Copyright © 2006 John Wiley & Sons, Ltd.

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  • Xin Zhang & Ming Zhou & Junyi Guo, 2007. "Optimal combinational quota‐share and excess‐of‐loss reinsurance policies in a dynamic setting," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 23(1), pages 63-71, January.
    • Handle: RePEc:wly:apsmbi:v:23:y:2007:i:1:p:63-71
    DOI: 10.1002/asmb.637
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    Cited by:

    1. Guan, Huiqi & Liang, Zongxia, 2014. "Viscosity solution and impulse control of the diffusion model with reinsurance and fixed transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 109-122.
    2. Li, Peng & Zhou, Ming & Yao, Dingjun, 2022. "Optimal time for the excess of loss reinsurance with fixed costs," International Review of Economics & Finance, Elsevier, vol. 79(C), pages 466-475.
    3. Matteo Brachetta & Claudia Ceci, 2019. "Optimal Excess-of-Loss Reinsurance for Stochastic Factor Risk Models," Risks, MDPI, vol. 7(2), pages 1-23, May.
    4. Zhang, Nan & Jin, Zhuo & Qian, Linyi & Fan, Kun, 2019. "Stochastic differential reinsurance games with capital injections," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 7-18.
    5. Matteo Brachetta & Claudia Ceci, 2019. "Optimal excess-of-loss reinsurance for stochastic factor risk models," Papers 1904.05422, arXiv.org.
    6. Guan, Guohui & Hu, Xiang, 2022. "Equilibrium mean–variance reinsurance and investment strategies for a general insurance company under smooth ambiguity," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    7. Danping Li & Dongchen Li & Virginia R. Young, 2017. "Optimality of Excess-Loss Reinsurance under a Mean-Variance Criterion," Papers 1703.01984, arXiv.org, revised Mar 2017.
    8. Liang, Xiaoqing & Liang, Zhibin & Young, Virginia R., 2020. "Optimal reinsurance under the mean–variance premium principle to minimize the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 128-146.

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