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Optimal Reinsurance-Dividend Strategy with Fixed Transaction Costs in a Regime-Switching Brownian Risk Model: A Viscosity Solution to the Impulse Control Problem

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  • Wenyuan Wang
  • Zuo Quan Xu
  • Kaixin Yan

Abstract

We consider a problem of optimal proportional reinsurance-dividend distribution under a Brownian risk model, where both the drift and volatility coefficients are subject to endogenous regime-switching. Dividend payments are subject to fixed transaction costs. The problem is formulated as a two-dimensional stochastic control problem, and we prove that the value function is the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation with nonlocal operator. For almost all parameter configurations, we explicitly characterize the optimal strategy that maximizes the expected total discounted dividends net of transaction costs until ruin. The optimal dividend policy is a two-barrier impulsive strategy, while the optimal reinsurance proportion is given in feedback form. Numerical examples are provided to illustrate the optimality results.

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  • Wenyuan Wang & Zuo Quan Xu & Kaixin Yan, 2026. "Optimal Reinsurance-Dividend Strategy with Fixed Transaction Costs in a Regime-Switching Brownian Risk Model: A Viscosity Solution to the Impulse Control Problem," Papers 2609.32686, arXiv.org.
    • Handle: RePEc:arx:papers:2609.32686
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    References listed on IDEAS

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    2. Zhengjun Jiang & Martijn Pistorius, 2012. "Optimal dividend distribution under Markov regime switching," Finance and Stochastics, Springer, vol. 16(3), pages 449-476, July.
    3. Mi Chen & Kam Chuen Yuen & Wenyuan Wang, 2021. "Optimal reinsurance and dividends with transaction costs and taxes under thinning structure," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2021(3), pages 198-217, March.
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    5. Bjarne Højgaard & Søren Asmussen & Michael Taksar, 2000. "Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation," Finance and Stochastics, Springer, vol. 4(3), pages 299-324.
    6. Chonghu Guan & Zuo Quan Xu & Rui Zhou, 2023. "Dynamic Optimal Reinsurance and Dividend Payout in Finite Time Horizon," Mathematics of Operations Research, INFORMS, vol. 48(1), pages 544-568, February.
    7. Hans Gerber & Elias Shiu, 2006. "On Optimal Dividend Strategies In The Compound Poisson Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 76-93.
    8. Martin Hunting & Jostein Paulsen, 2013. "Optimal dividend policies with transaction costs for a class of jump-diffusion processes," Finance and Stochastics, Springer, vol. 17(1), pages 73-106, January.
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