带比例交易成本的Lévy风险模型中的最优分红和注资  

Optimal dividend and capital injection in Lévy risk model with proportional transaction cost

作　　者：候力佳 胡华 HOU Lijia;HU Hua(School of Mathematical Statistics,Ningxia University,Yinchuan Ningxia 750021)

机构地区：[1]宁夏大学数学统计学院,宁夏银川750021

出　　处：《宁夏师范学院学报》2022年第10期101-112,共12页Journal of Ningxia Normal University

基　　金：宁夏回族自治区自然科学基金项目(2021AAC03030).

摘　　要：考虑了带比例交易成本的Lévy风险模型中分红只能发生在独立泊松过程跳跃时刻约束下的最优分红和注资问题,目的是最大化股息的预期净现值减去资本注入的成本.假设Lévy风险过程中分红策略是周期障碍策略,通过构造尺度函数求解值函数,利用Lévy过程的波动恒等式刻画了障碍值和周期障碍策略并进行验证.结果表明周期障碍策略是最优的.This paper considers the optimal dividend and capital injection problem in Lévy risk model with proportional transaction cost which can only occur under the constraint of the jump time of independent Poisson process.The objective is to maximize the expected net present value of dividends minus the costs of capital injection.Assuming that the dividend strategy in Lévy risk process is a periodic barrier strategy, the scale function is constructed to solve the value function, and the barrier value and periodic barrier strategy are characterized and verified by using the fluctuation identity of Lévy process.The results show that the periodic barrier strategy is optimal.

关 键 词：LÉVY过程 尺度函数 周期障碍策略 分红 注资 

分 类 号：O211.67[理学—概率论与数理统计]