投资收益随机的风险过程的绝对破产概率 Alternative Title Absolute ruin probabilities for a risk process with stochastic return on investments 靳晓忆 Thesis Advisor 牛明飞 2011-05-19 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 绝对破产 投资 赤字分布 莱维过程 微积分方程 Abstract 作为保险精算学核心内容的破产理论自Lundberg创立以来受到广泛的关注，现在已得到很大的发展，其中既可投资又可贷款的风险模型吸引了当代很多学者专家的研究。在这篇论文中，我首先对风险模型的意义、发展历程、及发展现状做了研究，然后在此基础上对一个更接近现实的风险过程进行探索研究。该过程资产盈余有两个来源：一是保险业务，它服从经典风险过程，二是投资业务，将盈余进行连续投资，投资收益率服从莱维过程。本文对该风险模型的破产问题进行研究，用一种新的方法导出了该风险过程在破产时刻的资本金分布即破产赤字分布的微积分方程以及破产概率的微积分方程，然后首次推导出了该过程绝对破产概率微积分方程组并给出了索赔额分布满足指数分布时绝对破产概率的较简洁的微积分表达式，最后对结论的优缺点进行分析，对未来发展做出展望。 Other Abstract The bankruptcy theory as the core content of insurance actuarial science from Lundberg founding has been widespread concerned. Now, it has got great development. The risk model that can both investment and loan attracted many scholars and experts to research. In this paper I have researched the significance, the development’s history and the actual state of the risk processes, then I introduce a new risk process .In the process surplus has two sources: First, the insurance industry, which obey the classical risk process, and second, investment income, yield obedience Levy process, we derive the integro-differential equation of surplus distribution function in ruin and that of the ruin probability, then, we derive an expression of absolute ruin probability. Finally, I analyze the conclusion and describe the development of the future. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/224641 Collection 数学与统计学院 Recommended CitationGB/T 7714 靳晓忆. 投资收益随机的风险过程的绝对破产概率[D]. 兰州. 兰州大学,2011.
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