【摘要】：保險定價問題是保險學研究中的核心問題之一,傳統(tǒng)的保險定價問題都是建立在概率統(tǒng)計與隨機過程的理論基礎之上�？紤]到?jīng)Q策者對市場形式的主觀判斷具有主觀性的特點,本文引入模糊數(shù)學的思想來處理保險定價問題。 一方面,以保險定價中經(jīng)典的Myers-Cohn模型為基礎,引入模糊變量,對經(jīng)典模型進行模糊化處理,得到了關于模糊MC保費的方程,并運用模糊數(shù)的相關運算法則,通過迭代的方法求解模糊保費。求解模型得到的模糊保費給出了可接受的保費價格的范圍,有利于決策者在可接受的范圍內(nèi)考慮多方面的因素,最終確定具體保費價格。 另一方面,針對經(jīng)典的Myers-Cohn模型將保險公司所有稅賦轉(zhuǎn)嫁給投保人、加大投保人投資風險的缺陷,本文改進了原有模型,提出將保險公司的部分投資收益回饋給投保人,而最終體現(xiàn)在保費價格的下調(diào)。對于保險公司投資收益的估計,本文引入最優(yōu)模糊投資組合的方法,以模糊滿意約束度作為投資風險水平的衡量標準,在給定風險承受水平下,根據(jù)模糊數(shù)學的相關性質(zhì),將模糊規(guī)劃模型轉(zhuǎn)化為確定線性規(guī)劃問題,求解最優(yōu)收益率。 最后本文構造了一個能同時包含隨機和模糊信息的隸屬函數(shù),其中,隨機信息體現(xiàn)在最優(yōu)收益率,而模糊信息體現(xiàn)在隸屬函數(shù)的模糊程度,并將新形式的隸屬函數(shù)引入到改進的模糊MC模型中,求解出能包含更多信息的保費價格。
[Abstract]:Insurance pricing problem is one of the core problems in insurance research. The traditional insurance pricing problem is based on the theory of probability statistics and stochastic process. Considering that the subjective judgment of market form by decision makers is subjective, this paper introduces the idea of fuzzy mathematics to deal with the problem of insurance pricing. On the one hand, based on the classical Myers-Cohn model in insurance pricing, fuzzy variables are introduced to fuzzify the classical model, and the equation of fuzzy MC premium is obtained, and the related algorithm of fuzzy number is used. The fuzzy premium is solved by iterative method. The fuzzy premium obtained by solving the model gives the range of acceptable premium price, which is helpful for decision makers to consider many factors in the acceptable range and finally determine the specific premium price. On the other hand, in view of the defect that the classical Myers-Cohn model passes on all the taxes of the insurance company to the policy holder and increases the investment risk of the policy holder, this paper improves the original model and proposes to return some of the investment income of the insurance company to the policy holder. And ultimately reflected in the reduction of premium prices. For the estimation of investment return of insurance companies, this paper introduces the optimal fuzzy portfolio method, takes the fuzzy satisfactory constraint degree as the measure standard of investment risk level, under the given risk bearing level, according to the related properties of fuzzy mathematics, The fuzzy programming model is transformed into a linear programming problem and the optimal rate of return is solved. Finally, a membership function which can contain both random and fuzzy information is constructed, in which the random information is embodied in the optimal rate of return, and the fuzzy information is embodied in the fuzzy degree of the membership function. The new form of membership function is introduced into the improved fuzzy MC model to solve the premium price which can contain more information.
【學位授予單位】：中南大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：F840.4

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