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On the optimality of double barrier strategies for Lévy processes

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  • Noba, Kei

Abstract

This paper studies de Finetti’s optimal dividend problem with capital injection. We confirm the optimality of a double barrier strategy when the underlying risk model follows a Lévy process that may have positive and negative jumps. In contrast with the spectrally one-sided cases, double barrier strategies cannot be handled by using scale functions to obtain some properties of the expected net present values (NPVs) of dividends and capital injections. Instead, to obtain these properties, we observe changes in the sample path (and the associated NPV) when there is a slight change to the initial value or the barrier value.

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  • Noba, Kei, 2021. "On the optimality of double barrier strategies for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 73-102.
    • Handle: RePEc:eee:spapps:v:131:y:2021:i:c:p:73-102
    DOI: 10.1016/j.spa.2020.08.008
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    Cited by:

    1. Wenyuan Wang & Yuebao Wang & Ping Chen & Xueyuan Wu, 2022. "Dividend and Capital Injection Optimization with Transaction Cost for Lévy Risk Processes," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 924-965, September.
    2. Noba, Kei, 2023. "On the optimality of the refraction–reflection strategies for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 174-217.

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