【作者】 高明美；

【导师】 赵明清；

【作者基本信息】 山东科技大学 ， 应用数学， 2003， 硕士

【摘要】 本文主要讨论了两类离散时间风险模型的破产问题： 首先，对含有投资利率和通货膨胀率的离散时间风险模型进行了研究。通过构造鞅并使用鞅的有关性质，得到了最终破产概率所满足的Lundberg不等式及其一般公式，并利用递推方法对该模型作了比较全面地探讨，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、破产前最大盈余的分布、破产时赤字的分布，以及三者的联合分布。另外，还讨论了盈余首次穿过给定水平时刻的分布。 其次，对经典的离散时间风险模型即复合二项离散时间风险模型作了进一步地探讨。利用鞅的概念，得到了该模型下的最终破产概率、盈余首次和末次达到给定水平时刻的分布。更多还原

【Abstract】 In this paper, the rum problems of two types of discrete time risk models are mainly discussed.Firstly, the discrete time risk model with the interest of investment and the rate of inflation is considered. By constructing martingale and using its properties, the paper gets Lundberg inequality of the ultimate ruin probability and the general formulas. Moreover, By using the recursive method, a lot of the 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 and the maximum surplus before ruin, the distribution of deficit at ruin, the joint distribution of surplus before and at ruin and the maximum surplus before ruin are obtained. In addition, the distribution of the time when the surplus process reaches a given level for the first time is obtained.Secondly, the classical discrete time risk model, namely, the compound binomial risk model is further discussed. Using the notion of martingale, the paper obtains the ultimate ruin probability and the distributions of the first and the last arrival time of a given level.更多还原