本文選題：遞推信度模型 + 最大熵��； 參考：《新疆大學》2017年碩士論文

【摘要】：信度理論就是研究如何根據(jù)歷史索賠額來解決保險費率的合理制定問題,在非壽險精算和保險實務中對下個時期的保費定價具有重要意義,主要是通過結(jié)合單個投保人的索賠經(jīng)驗數(shù)據(jù)與其他保單組合過去索賠經(jīng)驗數(shù)據(jù)來計算未來保費的一種定量方法,這種方法被廣泛的應用于保險的各個領(lǐng)域,一般情況下,所得的保費為個體保費與集體保費的加權(quán)和.一方面,本文在遞推信度模型的基礎(chǔ)上,結(jié)合最大熵方法,得到了最大熵方法下的遞推信度模型,考慮均方誤差最小和熵最大原則,進行兩次優(yōu)化得到未來保費以及遞推信度模型中信度因子的表達式,并且得到兩種特殊的權(quán)重結(jié)構(gòu):一種是年份較近的索賠額有較大的權(quán)重另一種是年份較遠的索賠額有較大的權(quán)重.另一方面,采用經(jīng)典信度理論得到的信度保費均是純保費原理下得到的,不具有保費的安全負荷,本文將在Esscher損失函數(shù)下,假設未來索賠具有推廣后的遞推形式,然后建立Esscher損失函數(shù)下的遞推信度模型以及廣義加權(quán)Esscher損失函數(shù)下的遞推信度模型.最后,在實際中,保險合同之間的索賠具有某種相依性,本文將對相依結(jié)構(gòu)的多合同信度模型作進一步的研究,包括齊次和非齊次的情況.
[Abstract]:The reliability theory is to study how to solve the problem of how to make the insurance rate reasonably according to the historical claim amount, which is of great significance to the premium pricing in the next period in the non-life insurance actuarial and insurance practice.It is a quantitative method to calculate the future premium mainly by combining the individual policyholder's claim experience data with other policies' combination of the past claim experience data. This method is widely used in various fields of insurance, generally speaking,The premium is the weighted sum of individual premium and collective premium.On the one hand, on the basis of the recursive reliability model and combined with the maximum entropy method, the recursive reliability model under the maximum entropy method is obtained, and the minimum mean square error and the maximum entropy principle are considered.Two optimizations are carried out to obtain the expressions of the future premium and the CITIC factor of the recursive reliability model.Two special weight structures are obtained: one is that the claim amount with a near year has a larger weight, and the other is that the claim amount with a longer year has a larger weight.On the other hand, the reliability premiums obtained by the classical reliability theory are all obtained under the pure premium principle and do not have the safety load of the premium. In this paper, under the Esscher loss function, we assume that the future claims have a generalized recursive form.Then the recursive reliability model under the Esscher loss function and the recursive reliability model under the generalized weighted Esscher loss function are established.Finally, in practice, the claims between insurance contracts have some dependence. In this paper, we will further study the multi-contract reliability model of dependent structures, including homogeneous and non-homogeneous cases.
【學位授予單位】：新疆大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：F224;F840.4

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