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Optimality of threshold strategies for spectrally negative Levy processes and a positive terminal value at creeping ruin

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  • Chongrui Zhu

Abstract

This paper investigates a dividend optimization problem with a positive creeping-associated terminal value at ruin for spectrally negative Levy processes. We consider an insurance company whose surplus process evolves according to a spectrally negative Levy process with a Gaussian part and a finite Levy measure. Its objective function relates to dividend payments until ruin and a creeping-associated terminal value at ruin. The positive creeping-associated terminal value represents the salvage value or the creeping reward when creeping happens. Owing to formulas from fluctuation theory, the objective considered is represented explicitly. Under certain restrictions on the terminal value and the surplus process, we show that the threshold strategy should be the optimal one over an admissible class with bounded dividend rates.

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  • Chongrui Zhu, 2021. "Optimality of threshold strategies for spectrally negative Levy processes and a positive terminal value at creeping ruin," Papers 2107.06841, arXiv.org, revised Jan 2023.
    • Handle: RePEc:arx:papers:2107.06841
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    References listed on IDEAS

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    1. Zhu, Jinxia, 2014. "Dividend Optimization For A Regime-Switching Diffusion Model With Restricted Dividend Rates," ASTIN Bulletin, Cambridge University Press, vol. 44(2), pages 459-494, May.
    2. Yin, Chuancun & Wen, Yuzhen, 2013. "Optimal dividend problem with a terminal value for spectrally positive Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 769-773.
    3. Chuancun Yin & Yuzhen Wen, 2013. "Optimal dividends problem with a terminal value for spectrally positive Levy processes," Papers 1302.6011, arXiv.org.
    4. Irmina Czarna & Zbigniew Palmowski, 2014. "Dividend Problem with Parisian Delay for a Spectrally Negative Lévy Risk Process," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 239-256, April.
    5. Kei Noba & Jos'e-Luis P'erez & Xiang Yu, 2019. "On the bail-out dividend problem for spectrally negative Markov additive models," Papers 1901.03021, arXiv.org, revised Feb 2020.
    6. Jiang, Zhengjun, 2019. "Optimal dividend policy when risk reserves follow a jump–diffusion process with a completely monotone jump density under Markov-regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 1-7.
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