随机利率下的保险精算模型

发布时间：2018-06-21 14:46

本文选题：盈余过程 + 利率　；参考：《大连理工大学》2005年硕士论文

【摘要】：保险,作为商品社会中处理风险的一种有效方法,已被世界普遍采纳.在现代保险业的发展中,科学的理论方法,特别是精算理论起着十分重要的作用.我国现已加入 WTO,但保险业与国际接轨还有很大的差距,迫切需要引进国际先进的保险精算理论, 并结合我国实际情况加以运用.传统的精算理论中,我们都是假定利率是确定的,然而实际上利率具有随机性,寿险中的利率随机性是风险产生的重要原因.利率波动时产生的风险,对于保险公司来说是致命的.为此,本文建立了随机利率下的综合人寿保险模型. 本文在一般的保险风险模型的基础上,阐述了固定利率下模型和结果,进一步考虑了随机利率因素,得到了随机利率下的连续时间模型和离散时间模型并计算出破产概率,保险公司破产前最大盈余分布,破产前盈余、破产后赤字与破产前最大盈余的联合分布以及盈余首次达到某一水平x的时间分布问题,使得相应的破产概率及其他结论更加具有实际意义,可作为保险公司预警系统的一个重要指标.另外,本文还讨论了一类视利息力函数为一个布朗运动过程的随机利率寿险模型,同时对寿险理论中的连续生存年金和矩以及保费计算进行了研究.本文随机利率的引进,降低了保险公司的风险程度,保险的公平性等原则也同时得到了较好的体现.保险公司通过参数的组合选择,在得到不同的随机利率下的保险产品的同时建立了随机优化保险模型.
[Abstract]:Insurance, as an effective way to deal with risks in commodity society, has been widely adopted in the world. In the development of modern insurance industry, scientific theoretical methods, especially actuarial theory, play a very important role. China has now joined the WTO, but there is still a big gap between the insurance industry and the international community. It is urgent to introduce international advanced actuarial theory and apply it according to the actual situation of our country. In the traditional actuarial theory, we all assume that the interest rate is determined, but in fact the interest rate is random, the interest rate randomness in the life insurance is the important reason for the risk. The risks that arise when interest rates fluctuate are fatal to insurance companies. Therefore, this paper establishes the model of comprehensive life insurance under random interest rate. On the basis of general insurance risk model, this paper expounds the model and results under fixed interest rate, and further considers the factor of stochastic interest rate. In this paper, the continuous time model and discrete time model under stochastic interest rate are obtained, and the probability of bankruptcy, the distribution of maximum surplus before bankruptcy, and the surplus before bankruptcy of insurance company are calculated. The joint distribution of the deficit after bankruptcy and the maximum surplus before bankruptcy and the time distribution of the surplus reaching a certain level x for the first time, It makes the corresponding ruin probability and other conclusions more meaningful and can be used as an important index of early warning system for insurance companies. In addition, a stochastic interest rate life insurance model with apparent interest force function as a Brownian motion process is also discussed. At the same time, the continuous survival annuity, moment and premium calculation in life insurance theory are studied. In this paper, the introduction of random interest rate reduces the risk of insurance companies, insurance fairness and other principles are also better reflected. The insurance company establishes the stochastic optimization insurance model while obtaining the insurance product under different random interest rate through the combination choice of the parameters.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2005
【分类号】：F224

【参考文献】