本文選題：聯(lián)合壽險　切入點：Markov模型　出處：《安徽工程大學(xué)》2013年碩士論文

【摘要】：隨著社會的發(fā)展,一個人投保已經(jīng)不能滿足整個家庭的需要,而為家庭內(nèi)的每個成員均投保又會增加家庭的負擔(dān).家庭聯(lián)合壽險將家庭內(nèi)的兩個(或兩個以上)成員作為聯(lián)合被保險人,該險種大大降低了保費額,同時又能讓參保的每個家庭成員享受保障.但在對聯(lián)合壽險的保單進行定價的時候,大多學(xué)者采用了簡單疊加的方法去處理各成員之間的關(guān)系.但實際上我們知道,一個家庭中各成員之間一定不會是簡單的獨立存在,各個體之間有著密不可分的關(guān)系,簡單的疊加處理會帶來較大的誤差.那么應(yīng)當(dāng)如何正確處理這種關(guān)系,Copula函數(shù)作為一種連接函數(shù),成為了學(xué)者們處理聯(lián)合壽險中個體間相關(guān)性的重要工具.Copula函數(shù)將一個聯(lián)合分布與該聯(lián)合分布的各個邊緣分布連接在一起,可以有效的處理隨機變量相依性結(jié)構(gòu)問題. 本文首先在家庭聯(lián)合壽險中考慮家庭因素,將一對夫妻生存狀況的未來發(fā)展構(gòu)造成Markov模型,考慮該模型內(nèi)各狀態(tài)的各種轉(zhuǎn)移方式,得到其轉(zhuǎn)移概率矩陣.再利用轉(zhuǎn)移強度與轉(zhuǎn)移概率的關(guān)系,得到該矩陣中各轉(zhuǎn)移概率的計算方法.然后用轉(zhuǎn)移概率表示出聯(lián)合生存狀態(tài)和最后生存者狀態(tài)的多生命精算函數(shù),由此得到家庭聯(lián)合壽險均衡年保費精算現(xiàn)值.但在此過程中,因為對個體間的關(guān)系簡單的采用了相互獨立的方法去處理,導(dǎo)致所得保費定價偏低.為了更符合實際情況,本文采用了改進的多生命函數(shù)符號,將單生命與二元生命精算符號的條件統(tǒng) .再結(jié)合二元條件Copula函數(shù),對條件阿基米德Copula函數(shù)進行改進,得到在統(tǒng)一條件下的條件阿基米德Copula函數(shù)及其生成元.再采用條件阿基米德Copula函數(shù)處理聯(lián)合壽險中個體間的相關(guān)性,對隨機利率下的家庭聯(lián)合壽險模型作出研究,得到其均衡年保費的精算現(xiàn)值.并給出了用不同方法處理個體相關(guān)性所得的均衡年保費精算現(xiàn)值的實例應(yīng)用. 本文做了如下工作： 1、將家庭聯(lián)合壽險中成員的未來生存狀態(tài)構(gòu)造成一個Markov模型,并將其作為家庭因素引入家庭聯(lián)合壽險精算模型中； 2、對傳統(tǒng)的多生命精算符號進行了改進,統(tǒng)一了單生命精算符號與多生命精算符號的條件；并在統(tǒng)一的條件下引入條件阿基米德Copula函數(shù)刻畫家庭聯(lián)合壽險中成員的相依關(guān)系； 3、針對上述兩種情況分別給出了家庭聯(lián)合壽險均衡年保費的定價方式,并通過實例分別與普通的家庭聯(lián)合壽險做了對比分析.
[Abstract]:With the development of society, one person's insurance can no longer meet the needs of the whole family. And insurance for every member of the family increases the burden on the family. The family union life insurance takes two (or more) members of the family as co-insured, which greatly reduces the amount of the premium. But when it comes to pricing a joint life insurance policy, most scholars use a simple superposition method to deal with the relationship between the members, but in fact we know that, The members of a family must not be simply independent of each other. Each individual is inextricably connected. A simple superposition process can lead to large errors. So how to correctly handle this relationship Copula function as a connection function, Copula function is an important tool to deal with the correlation between individuals in joint life insurance. The Copula function connects a joint distribution with each edge distribution of the joint distribution, which can effectively deal with the dependence structure of random variables. In this paper, the family factor is considered in the family joint life insurance, and the future development of a couple's living condition is constructed into a Markov model, and the various transfer modes of each state in the model are considered. The transfer probability matrix is obtained, and then the calculation method of each transition probability in the matrix is obtained by using the relation between the transfer intensity and the transition probability. Then, the multi-life actuarial function of the combined survival state and the last survivor state is expressed by the transfer probability. Thus, the actuarial present value of the equilibrium annual premium of the family joint life insurance is obtained. However, in the process, the relationship between individuals is simply treated by independent methods, which leads to the underpricing of the premium. In order to conform to the actual situation, In this paper, an improved multi-life function symbol is used to unify the conditions of the actuarial symbol of single life and binary life. Combining with the binary conditional Copula function, the conditional Archimedes Copula function is improved. The conditional Archimedes Copula function and its generator are obtained under unified conditions. Then the conditional Archimedes Copula function is used to deal with the correlation between individuals in joint life insurance, and the family joint life insurance model with random interest rate is studied. The actuarial present value of the equilibrium annual premium is obtained, and the application of the actuarial present value of the equilibrium annual premium obtained by different methods to deal with the individual correlation is given. This paper has done the following work:. 1. Construct a Markov model for the future survival status of the members in family joint life insurance, and introduce it into the actuarial model of family joint life insurance as a family factor; (2) the traditional multi-life actuarial symbol is improved to unify the conditions of single-life actuarial symbol and multi-life actuarial symbol, and the conditional Archimedes Copula function is introduced to describe the dependent relationship of the members in the family joint life insurance under the unified condition. 3. In view of the above two cases, the pricing method of the equilibrium annual premium of the family joint life insurance is given, and the comparison with the common family joint life insurance is made through the examples.
【學(xué)位授予單位】：安徽工程大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F840.4;F224

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