ABSTRACT

Maximising dividends is one classical stability criterion in actuarial risk theory. Motivated by the fact that dividends are paid periodically in real life, periodic dividend strategies were recently introduced (Albrecher et al. 2011). In this paper, we incorporate fixed transaction costs into the model and study the optimal periodic dividend strategy with fixed transaction costs for spectrally negative Lévy processes. The value function of a periodic $(b_u,b_l)$ strategy is calculated by means of exiting identities and Itô's excusion when the surplus process is of unbounded variation. We show that a sufficient condition for optimality is that the Lévy measure admits a density which is completely monotonic. Under such assumptions, a periodic $(b_u,b_l)$ strategy is confirmed to be optimal. Results are illustrated.

摘要

股息最大化是精算风险理论中的一项经典稳定性标准。受现实生活中定期支付股息这一事实的推动，最近引入了定期股息策略（Albrecher 等人，2011 年）。在本文中，我们将固定交易成本纳入模型，并研究具有固定交易成本的谱负 Lévy 过程的最优周期性股息策略。周期性的价值函数$({乙}_{你},{乙}_{升})$当剩余过程为无界变化时，策略是通过退出恒等式和伊藤免责计算的。我们证明了最优性的充分条件是 Lévy 测度允许一个完全单调的密度。在这样的假设下，定期$({乙}_{你},{乙}_{升})$策略被证实是最优的。结果被说明。