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Optimal reinsurance with both proportional and fixed costs

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  • Li, Peng
  • Zhou, Ming
  • Yin, Chuancun

Abstract

This paper investigates an optimal reinsurance problem with both proportional and fixed transaction costs. Associated with a reinsurance, the proportional cost is usually charged by the reinsurer and the fixed cost occurs at the beginning of the reinsurance due to consultant commission. We describe an insurer’s original cash reserve process by a Brownian motion with positive drift. The insurer aims to minimize its ruin probability by taking a dynamic reinsurance strategy. This leads to a mixed regular control and optimal stopping problem. We solve it by establishing a connection with an optimal stopping problem. The value function and the optimal reinsurance strategy are obtained explicitly.

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  • Li, Peng & Zhou, Ming & Yin, Chuancun, 2015. "Optimal reinsurance with both proportional and fixed costs," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 134-141.
    • Handle: RePEc:eee:stapro:v:106:y:2015:i:c:p:134-141
    DOI: 10.1016/j.spl.2015.06.024
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    References listed on IDEAS

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    Cited by:

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    2. 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.
    3. Liu, Bing & Meng, Hui & Zhou, Ming, 2021. "Optimal investment and reinsurance policies for an insurer with ambiguity aversion," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    4. Yan Zhang & Peibiao Zhao & Rufei Ma, 2022. "Robust Optimal Excess-of-Loss Reinsurance and Investment Problem with more General Dependent Claim Risks and Defaultable Risk," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2743-2777, December.
    5. Matteo Brachetta & Claudia Ceci, 2021. "Optimal Reinsurance Problem under Fixed Cost and Exponential Preferences," Mathematics, MDPI, vol. 9(4), pages 1-20, February.
    6. Yuxia Huang & Chuancun Yin, 2018. "A unifying approach to constrained and unconstrained optimal reinsurance," Papers 1807.06892, arXiv.org.
    7. Matteo Brachetta & Claudia Ceci, 2021. "Optimal reinsurance problem under fixed cost and exponential preferences," Papers 2101.04975, arXiv.org.

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