【作者】 邱萍；

【导师】 耿显民；

【作者基本信息】 南京航空航天大学 ， 概率论与数理统计， 2010， 硕士

【摘要】 风险理论的研究起源于瑞典精算师Lundberg,至今已有百年历史。随着保险公司经营规模的日益扩大和经营环境的不断变化,经典风险模型在很大程度上已不能模拟现实的风险状况。De Finetti于1957年率先提出了保险风险模型中的分红问题。红利的引入为保险公司的决策和经营提供了更多有价值的依据,特别地,为保险公司设计带红利的险种提供了理论依据。带分红的风险模型已经成为现代精算界和数学界研究的热门问题。为了与现代保险公司的实际需要相符,现代精算理论的很多研究是集中在随机环境下进行的。最近几年,对于一类更符合实际的变保费率的风险模型的研究也逐渐兴起。在考虑变保费率时,一般把保费率看成是风险自留的函数。除保费之外,利率因素对风险模型也有极大影响,带利率风险模型的研究也越来越引起人们的关注。本文在前人工作的基础上,首先考虑了带分红的连续时间复合二项风险模型,给出期望折罚函数的递推式,破产前瞬时盈余和破产赤字的矩以及破产时刻的Laplace变换;接着对带有马氏调控利率、变保费率的复合Pascal模型及分红问题进行了研究,给出破产概率满足的递推式及破产时刻、破产前瞬时盈余、破产赤字等精算量联合分布满足的积分方程。更多还原

【Abstract】 Studies of the risk theory were originated from the Sweden actuary Lundberg one hundred years ago. With the development of financial market and the change of the business environment of insurance company, the classical risk model can’t describe the real risk profile to a large extent. Dividend strategies for insurance risk models were firstly proposed by De Finetti in a paper presented to the International Congress of Actuaries in New York in 1957. Obviously, the theories about dividend strategies are very valuable in the devising and managing of products with dividends. The model with paying dividends has become a hot issue in the field of the modern actuarial science and mathematics. Correspond to the modern insurance company’s actual need, many research in modern actuarial theory are focused on the random environment. The study of the risk model with varying premiums rate which fits the fact more precisely is also arising. Considering the variable premium rate, the premium rate is generally regarded as the function of surplus. Besides the premium rate, risk models with interest also have been studied by many researchers.In this paper, we firstly study the expected discounted penalty function, the moments of surplus before ruin and deficit at ruin, and the Laplace transform of ruin time in the continuous-time compound binomial risk model with paying dividends; then we consider the compound Pascal model with paying dividends and variable premium under stochastic interest rates, we study the ruin probability and the joint distributions of this model.更多还原