On the spectrally negative Lévy risk process with mixed dividends and capital injections

Hua Dong, Xianghua Zhao and Hongshuai Dai

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 22, 7318-7335

Abstract: In this article, we study the spectrally negative Lévy risk process with mixed dividends and capital injections. Given a spectrally negative Lévy risk process with two boundaries and a sequence of random observation times, it is reflected at the lower boundary 0 and refracted at the upper boundary b(>0). Additionally, whenever the observed surplus is above b, all the excess is paid out as dividends. Using the scale function, we compute the expected discounted dividends and the expected discounted capital injections. The optimal dividend strategy is also discussed on maximizing the expected dividends subtracted by the discounted cost of capital injections. Numerical examples are presented to illustrate our results.

Date: 2025
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DOI: 10.1080/03610926.2025.2473605

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