【作者】 陈贵磊；

【导师】 赵明清；

【作者基本信息】 山东科技大学 ， 应用数学， 2005， 硕士

【摘要】 本文主要讨论了几种离散风险模型的破产问题: 首先,对离散经典风险模型中的理赔次数推广为负二项随机序列,提出了复合负二项风险模型。利用复合负二项随机序列的性质研究了复合负二项风险模型初始资本为0时的最终生存概率、有限时间内的生存概率、最终破产概率的一般表达式及Lundberg不等式。此外,研究了盈余首次和末次到达给定水平的时刻分布及相应的期望和方差表达式。其次,将复合负二项风险模型中的保费收取次数推广为负二项随机序列,提出了复合双负二项风险模型,利用递推方法对该模型进行了比较全面的研究,得到了破产时刻的分布、破产持续时间的分布、有限时间内的破产概率、最终破产概率;得到了破产前盈余的分布以及Lundberg不等式。再次,对双险种复合负二项风险模型进行研究,给出了盈余过程的性质及最终破产概率的一般表达式。最后,对广义复合双险种负二项风险模型进行研究,得到了盈余过程的性质、初始准备金为零时的生存概率及破产概率的表达式。更多还原

【Abstract】 In this paper, the ruin problems of several types of discrete risk model are mainly discussed.Firstly, the claim number is generalized to a negative stochastic series, and compound negative risk model is given. By the properties of compound negative stochastic series, the survival probability is got when the initial capital is zero. "The paper also gets survival probability in finite time, ultimate ruin probability and Lundberg inequality. Furthermore, it obtains the distributions of the time that surplus reaches a given level for the first and the last time . Secondly, the compound negative risk model is generalized to the double compound negative risk model, by using the recursive method, a lot of theoretical problems are resolved, such as the distributions of the ruin time and the ruin lasting time, the ruin probability in finite time, the ultimate ruin probability. Furthermore, in this paper, the distributions of the surplus before ruin are obtained. Thirdly, a discrete insurance risk model of two-type claims is considered, the properties of surplus, the ultimate ruin probability and Lundberg inequality are got. Lastly, the paper also studies on a generalized discrete insurance risk model of two-type claims, the problems are resolved, such as the survival probability, ruin probability when the initial capital is zero and the ultimate ruin probability.更多还原