本文選題：隨機(jī)利率　切入點(diǎn)：生存年金　出處：《山東財(cái)經(jīng)大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：在精算理論的傳統(tǒng)研究中，，假定利率都是固定的，但是實(shí)際上利率具有一定的隨機(jī)性，它會隨著相關(guān)政策的變化和經(jīng)濟(jì)環(huán)境的改變而發(fā)生變動。在日益波動的金融市場環(huán)境和日益競爭激烈的壽險(xiǎn)市場環(huán)境下，利率風(fēng)險(xiǎn)的度量、預(yù)測與管理變得越來越重要，因此隨機(jī)利率下的壽險(xiǎn)精算研究，也逐漸成為了研究者和實(shí)務(wù)工作者關(guān)注的焦點(diǎn)之一。 本論文在總結(jié)概括己有研究成果的基礎(chǔ)上,分別采用反射布朗運(yùn)動與泊松過程結(jié)合、反射布朗運(yùn)動與負(fù)二項(xiàng)分布結(jié)合兩種利息力累積函數(shù)描述利率的隨機(jī)性，進(jìn)一步研究了常見的單生命和二元生命狀態(tài)下的連續(xù)型壽險(xiǎn)精算模型。關(guān)于單生命壽險(xiǎn)模型，我們研究了兩種利息力累積函數(shù)模型下單生命壽險(xiǎn)保單的精算現(xiàn)值、年繳純保費(fèi)、均衡純保費(fèi)責(zé)任準(zhǔn)備金、變額壽險(xiǎn)和生存年金精算現(xiàn)值，得到了連續(xù)型壽險(xiǎn)模型下它們的一般顯性表達(dá)；并以反射布朗運(yùn)動與泊松過程結(jié)合的利息力累積函數(shù)模型下定期壽險(xiǎn)和生存年金模型的結(jié)果為例，通過數(shù)據(jù)模擬分析探討了隨機(jī)利率模型中的參數(shù)對精算現(xiàn)值的影響。關(guān)于二元生命狀態(tài)壽險(xiǎn)模型，我們基于兩種利息力累積函數(shù)模型，考慮到個體之間相互獨(dú)立和存在Frank copula相依的的兩種情況，分別研究了二元聯(lián)合生存狀態(tài)和二元最后生存者狀態(tài)下的壽險(xiǎn)和生存年金的精算現(xiàn)值。
[Abstract]:In the traditional study of actuarial theory, it is assumed that the interest rate is fixed, but in fact the interest rate has a certain randomness. In the increasingly volatile financial market environment and the increasingly competitive life insurance market environment, the measurement, prediction and management of interest rate risk become more and more important. Therefore, the actuarial research of life insurance under random interest rate has gradually become one of the focus of researchers and practitioners. On the basis of summing up the existing research results, this paper describes the randomness of interest rate by combining the reflected Brownian motion with the Poisson process, the reflected Brownian motion with the negative binomial distribution and the cumulative function of interest force. In this paper, we further study the common actuarial models of continuous life insurance under the condition of single life and binary life. For the single life insurance model, we study the actuarial present value of life insurance policies for orders issued by two kinds of cumulative function models of interest force, and pay the annual net premium. The equilibrium pure premium liability reserve, the actuarial present value of variable life insurance and survival annuity, and the general explicit expression of them under the continuous life insurance model are obtained. The results of periodic life insurance and survival annuity model under the cumulative function model of interest force combined with reflected Brownian motion and Poisson process are taken as an example. The influence of the parameters in the stochastic interest rate model on the actuarial present value is discussed through the data simulation analysis. For the binary life state life insurance model, we base on two kinds of interest force accumulation function model. The actuarial present value of life insurance and survival annuity under the condition of binary joint survival and binary last survivor is studied, considering the two conditions of individual independence and the existence of Frank copula.
【學(xué)位授予單位】：山東財(cái)經(jīng)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F840.62;F224

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