The Time of Recovery and the Maximum Severity of Ruin in a Sparre Andersen Model
The Time of Recovery and the Maximum Severity of Ruin in a Sparre Andersen Model
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DOI：
10.1080/10920277.2008.10597533
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发表时间：
2008-10
影响因子：
1.4
通讯作者：
Shuanming Li
中科院分区：
文献类型：
--
作者：
Shuanming Li
摘要位相型分布是允许马尔可夫解释的最一般的一类分布。利用马尔可夫技术可以分析具有相位型索赔间隔时间或相位型索赔的Sparre Andersen风险模型，并且结果可以用紧凑的矩阵形式表示。所涉及的计算在实践中很容易编程。本文研究了一类具有阶段型索赔间隔时间的Sparre Andersen风险模型中与首次到达时间和破产时间相关的一些量。在前面的讨论中，作者得到了剩余过程从初始剩余到达给定目标的第一次的拉普拉斯变换的矩阵表达式。利用这一结果，我们分析了（1）破产后恢复时间的拉普拉斯变换，（2）破产前盈余达到一定水平的概率，（3）最大破产严重度的分布。我们还给出了一个矩阵表达式的期望贴现股息支付破产前的Sparre Andersen模型的存在下，一个常数的股息障碍。
Abstract Phase-type distributions are one of the most general classes of distributions permitting a Markovian interpretation. Sparre Andersen risk models with phase-type claim interarrival times or phase-type claims can be analyzed using Markovian techniques, and results can be expressed in compact matrix forms. Computations involved are readily programmable in practice. This paper studies some quantities associated with the first passage time and the time of ruin in a Sparre Andersen risk model with phase-type interclaim times. In an earlier discussion the present author obtained a matrix expression for the Laplace transform of the first time that the surplus process reaches a given target from the initial surplus. Using this result, we analyze (1) the Laplace transform of the recovery time after ruin, (2) the probability that the surplus attains a certain level before ruin, and (3) the distribution of the maximum severity of ruin. We also give a matrix expression for the expected discounted dividend payments prior to ruin for the Sparre Andersen model in the presence of a constant dividend barrier.