隨機(jī)利率下年金的精算模型

信息計算科學(xué)論文編號:XXLW109 論文字?jǐn)?shù):16580,頁數(shù):42

目錄
中文摘要…………………………………………………………………………………………………I
英文摘要……………………………………………………………..…………………………………II
目錄……………………………………………………………………………………………………III
第一章  年金問題的綜述……………………………………………………………………………....1
 1.1年金的基本概念………………………………………………………………………….……1
 1.2年金建立的好處…………………………………………………………………………….…2
 1.3年金計算方式…………………………………………………………………………….……3
 1.4精算學(xué)及其發(fā)展………………………………………………………………………….……3
 1.5年金中的數(shù)學(xué)原理………………………….…………………………………………………4
 1.6隨機(jī)利率情況下目前研究的狀況……………………………………………….……………5
 1.7本文研究的主要內(nèi)容…………………………………………………………….……………6
第二章  利息論基礎(chǔ)……………………………………………………………………………………7
 2.1  利息的度量…………………………………………………………..………………………7
     2.1.1積累函數(shù)與金額函數(shù)……………………………………………………….…………7
     2.1.2現(xiàn)值…………………………………………………………………………….………9
 2.1.3離散時間下的利息度量：利息率與貼現(xiàn)率……………………………….…………9
 2.1.4連續(xù)時間下的利息度量：利息力……………………………………………………10
 2.1.5單利與復(fù)利……………………………………………………………………………11
 2.2  年金…………………………………………………………………………………….……12
     2.2.1年金的定義……………………………………………………………………………12
     2.2.2年金的分類……………………………………………………………………………12
     2.2.3常見的確定年金………………………………………………………………………12
第三章  隨機(jī)利率相關(guān)知識 ……………………………………………………………….…………16
 3.1  離散時間下的隨機(jī)利息………………………………………………………….…………16
     3.1.1獨(dú)立同分布的情形……………………………………………………………………16
 3.1.2時間序列模型…………………………………………………………………………17
 3.2  連續(xù)時間下的隨機(jī)利息………………………………………………………….…………20
 3.3  其它在本文中用到的知識(舉例分析------生存年金精算模型)…………….…………22
 3.3.1 歲生命的剩余壽命[8]…………………………………………………….…………22
 3.3.2死亡力…………………………………………………………………………………23
 3.3.3Wiener過程……………………………………………………………………………24
第四章  隨機(jī)利率下的綜合年金模型…………………………………………………...……………25
 4.1  利率對年金的影響…………………………………………….……………………………25
 4.2  模型的建立………………………………………….………………………………………25
     4.2.1年金責(zé)任………………………………………………………………………………25
 4.2.2保費(fèi)計算………………………………………………………………………………25
 4.3  參數(shù)的取值范圍………………………………………………………….…………………34
 4.4  結(jié)論…………………………………………………………………….……………………34
第五章  展望…………………………………………………………………………...………………35
結(jié)束語…………………………………………………………………...………………………………36
致謝………………………………………………………………………...……………………………37
參考文獻(xiàn)…………………………………………………...……………………………………………38

摘要
 年金在日常生活中被廣泛應(yīng)用，但以往大多研究的是固定年金以及隨機(jī)利率下的確定年
金．本文考慮了利率隨機(jī)波動對生命年金的影響，運(yùn)用隨機(jī)利率模型，得出年金精算現(xiàn)值較為簡單的遞推關(guān)系式，并舉例說明利率的隨機(jī)波動對年金精算現(xiàn)值的影響程度，結(jié)果表明利率的波動對年金的定價影響非常大，不容忽視。
 年金是經(jīng)濟(jì)、金融、年金領(lǐng)域中的重要概念,隨機(jī)利率下關(guān)于年金問題的研究近年來引起了應(yīng)用概率統(tǒng)計界的極大關(guān)注,并且取得了一系列深刻的研究成果.由于隨機(jī)利率的復(fù)雜性和重要性,關(guān)于這一問題的研究方興未艾.文中試圖在隨機(jī)利率條件下研究年金現(xiàn)值的數(shù)字特征.基于隨機(jī)利率下的年金思想方法以及鞅、反射Brownian運(yùn)動和隨機(jī)序的理論,得到了控制隨機(jī)利率下連續(xù)年金現(xiàn)值的期望,并給出了離散隨機(jī)年金現(xiàn)值函數(shù)在凸序意義下的上界,討論了上界的分布函數(shù)和停止損失保費(fèi),進(jìn)而得到了離散的隨機(jī)年金現(xiàn)值的期望。
 
 關(guān)鍵字:年金 隨機(jī)利率 精算模型 期望 精算

Abstract
 
 Annuity is widely used in daily life, but past experience most of the fixed annuity, as well as stochastic interest rate determined under the annuity. This paper considers the random fluctuations in interest rates impact on life annuities, using stochastic interest rate model, obtained Annuity relatively simple recurrence relation, and illustrates the interest rate of the random fluctuations of the Annuity's impact, the results show that the interest rate The impact of fluctuations on the pricing of annuities is very large, can not be overlooked. random interest rate on the annuity issue of applied probability and statistics in recent years has aroused great concern to industry, and has made a series of profound research.
 Annuity is the economic, financial, insurance, important concepts in the field, As the complexity of stochastic interest rates and importance of research on this issue in full swing. This paper studied under stochastic interest rate annuity present value of the digital features. annuities under random rates of interest-based way of thinking and martingale, reflecting Brownian motion and random order of the theory, control stochastic interest rate the present value of expected continuous annuity, annuity given the present value of discrete random function in the sense of convex order upper bound on the community to discuss the distribution function and the stop-loss premiums, and then get the discrete random annuity is value expectations.
 Keywords: annuities   stochastic interest rates   actuarial model   expectations   actuarial