【摘要】：一直以來,保費價格都是保險理論和實踐中研究的核心問題.保險公司的業(yè)務可以用一個輸入輸出系統(tǒng)來描述,在這個系統(tǒng)中,盈余由征收的保費和賺取的利息以及投資收益而增加,由理賠和成本的支出而減少.保費定價過低會使保險公司陷入經營困境甚至會導致破產,定價過高會使保險公司降低市場競爭力且會增加被保險人負擔,因此保費定價對保險公司來說是非常重要的精算問題.保費的厘定就是求出一個最小保費,它不僅可以應付理賠,而且還使得保單組合的盈余足夠快增長.保費的厘定,對保險公司的生死存亡至關重要,因此,合理的風險定價模式,一直備受保險工作者和理論界廣泛關注. 本文首先從保費定價的基本理論入手,考慮了索賠額與等待時間是一組具有廣義FGM相依結構的序列,在復合泊松過程模型的假設下,對保費定價進行了深入的探索和研究,相對于索賠額與等待時間獨立的情形更加符合實際.在確定復合泊松過程下的廣義FGM Copula的分布函數后,求得出其概率密度函數,通過Laplace變換、Laplace逆變換等方法求出了索賠額的矩母函數的表達式,并對比了索賠額與等待時間獨立情形的矩母函數. 隨后文章進一步討論了矩母函數的高階導數計算方法,給出了其Esscher定價泛函的表達式,利用Matlab軟件對Esscher定價泛函與參數h之間的關系進行了數值模擬,并在零利息力和非零利息力下分別討論了凈保費的表達式. 最后,文章對全文的研究結果做了總結,并介紹了作者下一步的工作計劃.
[Abstract]:Premium price has always been the core issue of insurance theory and practice. The insurance company's business can be described as an input-output system in which earnings are increased by levied premiums and interest earned as well as investment returns and reduced by expenses for claims and costs. Too low premium pricing will put insurance companies into business difficulties or even lead to bankruptcy. Overpricing will make insurance companies less competitive in the market and increase the insurant's burden. Therefore, premium pricing is a very important actuarial issue for insurance companies. The premium is determined to work out a minimum premium, which not only pays for claims, but also makes the surplus of the policy portfolio grow fast enough. The determination of premium is very important to the life and death of insurance company. Therefore, the reasonable risk pricing model has been paid more and more attention by insurance workers and theorists. First of all, this paper starts with the basic theory of premium pricing, considering that the claim amount and waiting time are a series of generalized FGM dependent structures. Under the assumption of compound Poisson process model, the premium pricing is deeply explored and studied. The situation where the claim amount is independent of the waiting time is more realistic. After determining the distribution function of the generalized FGM Copula under the compound Poisson process, the probability density function is obtained, and the expression of the moment generating function of the claimed amount is obtained by means of Laplace transform and Laplace inverse transformation, etc. The moment generating function of claim amount and waiting time independent case is compared. Then, the calculation method of higher order derivative of moment generating function is discussed, the expression of Esscher pricing functional is given, and the relationship between Esscher pricing function and parameter h is numerically simulated by using Matlab software. The expressions of net premium are discussed under zero interest force and non zero interest force respectively. Finally, the paper summarizes the research results and introduces the author's next work plan.
【學位授予單位】：安徽工程大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：F840.31;F224

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本文編號：2444157