不同损失限制下的最优保费研究

发布时间：2018-08-07 16:51

【摘要】：从我国保险业的发展来看,保险对人们生活有着重要的意义。当被保险人由于风险事故而造成经济损失时,保险公司承担了全部或者部分的风险损失,被保险人可以得到来自保险公司的补偿。从而降低了被保险人的风险损失。但保险公司是以盈利为目的的金融服务业,因此选择合理的理赔方案,对于保险公司来说是至关重要的。本篇论文旨在讨论一种具有最大理赔限额且小损失下可以获得一定的赔偿的最优保险模型。文中在一定的限制条件下进行推导,得出这种理赔模型的性质和特点。同时与Zhou的理赔模型(模型1)进行比较,总结了本文中提出的保险理赔模型3的优缺点。本文开篇介绍了一些前人所研究的损失模型,并对一些模型进行了纯保费的计算,讨论了在不同的限制条件下模型对纯保费的影响情况。另外为了便于后文应用,还介绍了效用函数、风险厌恶系数等概念。论文最后提出了一种改进最低损失限制的保险理赔模型(具有曲度的最低限额和最高损失限制的保险模型)。并运用极大值原理,通过大量的计算、求导、作图,讨论在一定的条件下,参数d和δ对模型中的最优值的影响。最终总结出当本文提出的模型3中保单数是模型1中的保单数的N倍时(N在文章中有具体的公式表示),就可以使得两种模型收益相等,而如果保单数大于N倍时,模型3优于模型1。由于模型3在小额赔偿上具有一定的优越性,所以被保险人更容易选择模型3这种保险理赔模式。
[Abstract]:From the development of insurance industry in our country, insurance has important meaning to people's life. When the insured causes economic loss due to the risk accident, the insurance company bears all or part of the risk loss, and the insured can get the compensation from the insurance company. Thus reducing the risk loss of the insured. But the insurance company is the financial service industry aiming at profit, so it is very important for the insurance company to choose a reasonable settlement scheme. The purpose of this paper is to discuss an optimal insurance model with a maximum claim limit and a certain amount of compensation under small losses. In this paper, the properties and characteristics of the claim model are derived under certain restriction conditions. At the same time, compared with Zhou's claim model (model 1), the advantages and disadvantages of insurance claim model 3 proposed in this paper are summarized. At the beginning of this paper, we introduce some loss models studied by predecessors, calculate the pure premium of some models, and discuss the influence of the model on the pure premium under different restricted conditions. In addition, the concepts of utility function and risk aversion coefficient are also introduced in order to facilitate the later application. In the end, an improved insurance claim model with minimum loss limit and maximum loss limit is proposed. The influence of parameters d and 未 on the optimal value of the model is discussed under certain conditions by using the principle of maximum value through a large amount of calculation, derivation and drawing. Finally, it is concluded that when the singular number in model 3 is N times of the number of policies in model 1 (N is represented by a specific formula in this paper), the two models can get equal returns, but if the number of policies is greater than N, Model 3 is superior to model 1. Because model 3 has some advantages in small amount of compensation, it is easier for the insured to choose model 3.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.3;O211.67

【相似文献】