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Optimal periodic dividend strategies for spectrally negative Lévy processes with fixed transaction costs. (English) Zbl 1476.91119

The form of the optimal periodic dividend strategy with fixed transaction costs, when the dividend decisions are Poissonian and where the underlying model is a spectrally negative Lévy process, is determined in the paper. The value function of a periodic \((b_u, b_l)\) strategy concisely in terms of scale functions was possible to compute by extending the results of the paper [J.-L. Pérez and K. Yamazaki, “Mixed periodic-classical barrier strategies for Lévy risk processes”, Risks 6, No. 2, Article No. 33, 39 p. (2018; doi:10.3390/risks6020033)].
It was also confirmed that the periodic \((b*_u, b*_l )\) solution exists and is optimal, regarding an additional assumption that the Lévy measure has completely monotonic density and imposed the same two conditions as B. Avanzi et al. [Insur. Math. Econ. 93, 315–332 (2020; Zbl 1447.91126)] on the parameters \(b_u\) and \(b_l\).
We mention that periodic dividend strategies were recently introduced by H. Albrecher et al. [ASTIN Bull. 41, No. 2, 645–672 (2011; Zbl 1239.91072)], and that was motivated by the fact that dividends are paid periodically in real life.

MSC:

91G05 Actuarial mathematics
60G51 Processes with independent increments; Lévy processes
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References:

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