论文标题
巴黎的游览以资本注入进行抽奖反映的征税保险风险流程
Parisian excursion with capital injection for draw-down reflected Levy insurance risk process
论文作者
论文摘要
本文讨论了巴黎的毁灭问题,其中包括征收保险风险过程的资本注入。当盈余过程的抽签时间降至其最后一个记录最大记录的预先指定函数时,资本注入将在盈余过程的耗尽时间进行。不断支付资本,以使盈余保持在平局的水平上,直到盈余过程超过了记录高或发生巴黎人类型的毁灭性,这是因为首次注射资本以来,盈余过程是在独立指数期间均超过独立指数时期的记录。提出了有关游览的一些分布身份。首先,我们给出了巴黎的废墟概率和毁灭性时间固定水平以上的固定水平,剩余位置的剩余位置以及废墟的总资本注入的关节拉普拉斯变换(可能在第一次通道时被杀死)。其次,我们获得了在巴黎废墟中丧生的盈余过程的$ q $ - 电势量度。最后,我们给出了最高巴黎破产时间的总折扣资本付款总额的预期价值。结果是使用频谱征费过程的波动和偏移理论的最新发展得出的,并根据征费过程的规模函数明确地呈现。给出了一些数值示例,以促进对初始盈余和观察频率对破坏概率和预期总资本注入的影响的分析。
This paper discusses Parisian ruin problem with capital injection for Levy insurance risk process. Capital injection takes place at the draw-down time of the surplus process when it drops below a pre-specified function of its last record maximum. The capital is continuously paid to keep the surplus above the draw-down level until either the surplus process goes above the record high or a Parisian type ruin occurs, which is announced at the first instance the surplus process has undergone an excursion below the record for an independent exponential period of time consecutively since the time the capital was first injected. Some distributional identities concerning the excursion are presented. Firstly, we give the Parisian ruin probability and the joint Laplace transform (possibly killed at the first passage time above a fixed level of the surplus process) of the ruin time, surplus position at ruin, and the total capital injection at ruin. Secondly, we obtain the $q$-potential measure of the surplus process killed at Parisian ruin. Finally, we give expected present value of the total discounted capital payments up to the Parisian ruin time. The results are derived using recent developments in fluctuation and excursion theory of spectrally negative Levy process and are presented semi explicitly in terms of the scale function of the Levy process. Some numerical examples are given to facilitate the analysis of the impact of initial surplus and frequency of observation period to the ruin probability and to the expected total capital injection.