On the optimality of the refraction--reflection strategies for Levy processes
On the optimality of the refraction--reflection strategies for Levy processes
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折射的最优性--Levy过程的反射策略
DOI：
10.1016/j.spa.2023.02.006
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发表时间：
2023
影响因子：
1.4
通讯作者：
Noba Kei
中科院分区：
文献类型：
--
作者：
Mata Dante;Moreno-Franco Harold A.;Noba Kei;Perez Jose-Luis;Noba Kei
本文在股利策略绝对连续的假设下，研究了有资本注入的de Finetti最优股利问题。在以前的许多研究中，被控制之前的过程被假定为一个谱单边的Lévy过程，然而在本文中，我们使用的Lévy过程，可能有积极和消极的跳跃。在主要定理中，我们证明了折射-反射策略是最优策略。我们还提到了定义折射Lévy过程的随机微分方程解的存在性和唯一性。
In this paper, we study de Finetti’s optimal dividend problem with capital injection under the assumption that the dividend strategies are absolutely continuous. In many previous studies, the process before being controlled was assumed to be a spectrally one-sided Lévy process, however in this paper we use a Lévy process that may have both positive and negative jumps. In the main theorem, we show that a refraction–reflection strategy is an optimal strategy. We also mention the existence and uniqueness of solutions of the stochastic differential equations that define refracted Lévy processes.