一种新的死亡率模型及基于中国人口数据的比较分析

基于中国人口死亡率数据, 对APC模型进行扩展, 并将扩展的死亡率模型(EAPC模型)与APC模型和LC模型进行对比. 通过比较模型的拟合效果和预测效果, 并对其稳定性进行检验, 发现由APC模型扩展而来的EAPC模型更适合于拟合和预测中国的人口死亡率, 这为我国死亡率模型的使用提供了更多可行的方案.     

中国企业生命表矛盾现象的数学解释与启示

以企业生命周期理论为依据,对比分析中国企业生命表与中国人寿保险业经验生命表(1990-1993)(男女混合),提出中国企业生命表的矛盾现象,并对此现象做出了数学解释,得出这一矛盾现象是由于中国企业低龄的高死亡率造成的,并依此提出相应的几点启示.     

基于极值理论高龄死亡率模型的比较研究

基于极值理论模型,对中国与日本高龄人口死亡率进行拟合和预测,克服了其他死亡率参数外推模型的主观性.在极值理论高龄死亡率模型的基础上使用加权最小二乘法,通过反复试验方式选择最优门限年龄和模型参数估计值,并且预测中国与日本人口最高年龄以及最高年龄区间估计.此研究为我国经验生命表的编制工作提供借鉴.     

多总体死亡率差异风险度量——以ILS债券为例

在回顾多总体动态死亡率预测模型研究成果的基础上,简要评述了已有模型的适应情况和假设条件,并依此构建了死亡率差异风险的度量模型.此后,并以ILS债券为例,利用HMD数据库中英国和美国人口死亡率数据,使用构建的死亡率差异风险度量模型,测量了ILS债券中的死亡率差异风险.定量分析结果显示:ILS为投资者设定了较高的安全阀值,保障了ILS的成功发行.     

基于跳跃扩散死亡率模型的新型年金定价及其风险评估

由于各个年龄段的人口死亡率呈现出的明显下降趋势,依赖静态生命表的传统精算方法已经无法实现年金收支上真正的精算等价,这无疑会严重影响到保险公司的风险管理和稳健运营.因此文章尝试从死亡率的随机建模和死亡率衍生产品创新的角度来准确度量风险并进而厘清风险的权责和分摊.首先,文章将建立带跳跃过程的随机死亡率模型,以中国实际死亡率的历史数据,对模型参数进行最大似然估计,并运用Bootstrap方法对参数估计的精确程度进行检验;其次,文章在产品设计层面探讨动态的支付调整,即在年金产品中嵌入一个欧式死亡率期权,给予保险公司根据真实死亡率调整赔付额度的权利.文章的研究结果表明新型年金能够有效分散长寿风险,提高承保双方的效用,对促进商业年金的发展具有重要的现实意义和参考价值.     

中国城市人口死亡率的预测

死亡率是随时间变动的具有不确定性的变量,基本养老保险的养老金给付必须考虑动态死亡率的影响,因此需要对中国城市人口的未来死亡率变动进行预测。针对部分年的中国城市分性别人口死亡率数据缺失的实际状况,本文运用死亡人数服从Poisson分布的Lee-Carter模型进行了预测,结果表明该模型的拟合较好。由上述预测得出,随时间的延续,中国城市人口的预期寿命将明显增加,为基本养老保险的支付带来严重的风险,该风险导致基本养老保险个人账户的收入远不足以支付未来的养老金,必须引起重视。本文就如何规避这一风险给出了一些政策建议。     

关于2000-2003新生命表出台对寿险业的影响分析

随着2000-2003新生命表的出台, 寿险业对生命表的关注程度日益加强, 本文第一部分介绍了研究背景, 第二部分对死亡效力(mortality force)进行模拟, 并进行了可靠性检验. 第三部分结合中国人寿保险业1990-1993生命表、2000-2003生命表, 给出了时间推移下同年龄死亡效力之间的关系. 基于此, 引入了布朗运动的随机变量, 将死亡效力随机化, 并进行模拟, 优化了可靠性检验结果.第四部分预测了生命表改善对年金保险(annuity)净费率的影响, 分析了延期承保的费率影响趋势, 指出了长寿风险. 最后给出了相关评价及未来预测思路.     

基于Copula-AR(n)-LSV的死亡率建模及长寿风险度量

合理的死亡率模型是精准度量长寿风险的关键.考虑不同年龄组间死亡率的相依性以及各年龄组死亡率的自相关性和异方差结构,运用多元Copula和AR(n)-LSV模型构建了随机动态死亡率模型,并在此基础上进一步运用VaR、TVaR、GlueVaR对长寿风险进行测度.研究结果表明Copula-AR(n)-LSV模型比Lee-Cater模型更好地刻画了死亡率趋势和波动;死亡率随着时间的推移逐渐改善,个体将面临逐年增长的长寿风险.     

基于协整理论的中国人口死亡率预测

近年来,人类寿命明显延长.长寿风险对于国家养老金制度,保险公司寿险业务的影响日益凸现.长寿风险源于人口死亡率的非预期变动,精准预测人口死亡率是长寿风险研究的一项重要内容.文中提出了一种死亡率预测的新方法,将计量经济学中的协整理论引入死亡率预测,以弥补中国死亡率历史数据缺乏,并结合极值理论方法给出中国死亡率的预测.     

C-ROSS中长寿风险资本要求

为了应对长寿风险,保险公司需要对风险规模有清晰的认识.迄今为止,国内已有文献主要使用内部模型,针对中国保险公司的长寿风险做了度量.即将实施的C-ROSS为我国长寿风险度量提供了第一个标准模型,将是长寿风险度量的重要参考和强制标准.因此将在C-ROSS标准模型技术细节探讨的基础上,计算相应的长寿风险官方要求.根据文献梳理和究显示:长寿风险会给整个年金支付现值带来2~6%支付增加,其中由波动性长寿风险引发的支付增加为1.6~4%,其中(监管要求的)趋势性长寿风险引发的支付增加为1~3%.此外,与欧盟SolvencyⅡ相比,C-ROSS充分考虑了中国人口死亡率改善特点和未来发展趋势,在资本约束较强的背景下,设定了一个审慎、简洁的长寿风险资本要求.     

From regulatory life tables to stochastic mortality projections: The exponential decline model

Often in actuarial practice, mortality projections are obtained by letting age-specific death rates decline exponentially at their own rate. Many life tables used for annuity pricing are built in this way. The present paper adopts this point of view and proposes a simple and powerful mortality projection model in line with this elementary approach, based on the recently studied mortality improvement rates. Two main applications are considered. First, as most reference life tables produced by regulators are deterministic by nature, they can be made stochastic by superposing random departures from the assumed age-specific trend, with a volatility calibrated on market or portfolio data. This allows the actuary to account for the systematic longevity risk in solvency calculations. Second, the model can be fitted to historical data and used to produce longevity forecasts. A number of conservative and tractable approximations are derived to provide the actuary with reasonably accurate approximations for various relevant quantities, available at limited computational cost. Besides applications to stochastic mortality projection models, we also derive useful properties involving supermodular, directionally convex and stop-loss orders.     

Life Anuities with Stochastic Survival Probabilities: A Review

An insurance company selling life annuities has to use projected life tables to describe the survival of policyholders. Such life tables are generated by stochastic processes governing the future path of mortality. To fix the ideas, the standard Lee-Carter model for mortality projection is adopted here. In that context, the paper purposes to examine the consequences of working with random survival probabilities. Various stochastic inequalities are derived, showing that the risk borne by the annuity provider is increased compared to the classical independent case. Moreover, the type of dependence existing between the insured life times is carefully examined. The paper also deals with the computation of ruin probabilities and large portfolio approximations.      

A geostatistical approach for dynamic life tables: The effect of mortality on remaining lifetime and annuities

Dynamic life tables arise as an alternative to the standard (static) life table, with the aim of incorporating the evolution of mortality over time. The parametric model introduced by Lee and Carter in 1992 for projected mortality rates in the US is one of the most outstanding and has been used a great deal since then. Different versions of the model have been developed but all of them, together with other parametric models, consider the observed mortality rates as independent observations. This is a difficult hypothesis to justify when looking at the graph of the residuals obtained with any of these methods.Methods of adjustment and prediction based on geostatistical techniques which exploit the dependence structure existing among the residuals are an alternative to classical methods. Dynamic life tables can be considered as two-way tables on a grid equally spaced in either the vertical (age) or horizontal (year) direction, and the data can be decomposed into a deterministic large-scale variation (trend) plus a stochastic small-scale variation (residuals).Our contribution consists of applying geostatistical techniques for estimating the dependence structure of the mortality data and for prediction purposes, also including the influence of the year of birth (cohort). We compare the performance of this new approach with different versions of the Lee-Carter model. Additionally, we obtain bootstrap confidence intervals for predicted q_xt resulting from applying both methodologies, and we study their influence on the predictions of e_65t and a_65t.     

Bayesian graduation of mortality rates: An application to reserve evaluation

This paper presents Bayesian graduation models of mortality rates, using Markov chain Monte Carlo (MCMC) techniques. Graduated annual death probabilities are estimated through the predictive distribution of the number of deaths, which is assumed to follow a Poisson process, considering that all individuals in the same age class die independently and with the same probability. The resulting mortality tables are formulated through dynamic Bayesian models. Calculation of adequate reserve levels is exemplified, via MCMC, making use of the value at risk concept, demonstrating the importance of using “true” observed mortality figures for the population exposed to risk in determining the survival coverage rate.     

Modelling and forecasting mortality in Spain

Experience shows that static life tables overestimate death probabilities. As a consequence of this overestimation the premiums for annuities, pensions and life insurance are not what they actually should be, with negative effects for insurance companies or policy-holders. The reason for this overestimation is that static life tables, through being computed for a specific period of time, cannot take into account the decreasing mortality trend over time. Dynamic life tables overcome this problem by incorporating the influence of the calendar when graduating mortality. Recent papers on the topic look for the development of new methods to deal with this dynamism.     

Forecasting and simulating mortality tables

In this paper we suggest solutions to the actuaries, facing the problem of estimating future mortality tables, especially in cases where there is a lack of relevant data and where the tendencies are not easy to estimate directly. We propose the utilization of external sources of information in the form of other, published mortality tables and use formal statistical tests to decide among these possible candidates. The procedure can also be applied for checking e.g. the goodness of mortality selection factors. We suggest the use of parametric families in modelling; for example the simple 2-parameter Azbel model. We conclude the paper by a simulation study which allows for the quantification of the possible risks related to unforeseen changes in the mortality tables in the future. To calibrate the variances of these models, initial estimates are needed, which we get by the Lee–Carter method.     

Longevity risk management for life and variable annuities: The effectiveness of static hedging using longevity bonds and derivatives

For many years, the longevity risk of individuals has been underestimated, as survival probabilities have improved across the developed world. The uncertainty and volatility of future longevity has posed significant risk issues for both individuals and product providers of annuities and pensions. This paper investigates the effectiveness of static hedging strategies for longevity risk management using longevity bonds and derivatives (q-forwards) for the retail products: life annuity, deferred life annuity, indexed life annuity, and variable annuity with guaranteed lifetime benefits. Improved market and mortality models are developed for the underlying risks in annuities. The market model is a regime-switching vector error correction model for GDP, inflation, interest rates, and share prices. The mortality model is a discrete-time logit model for mortality rates with age dependence. Models were estimated using Australian data. The basis risk between annuitant portfolios and population mortality was based on UK experience. Results show that static hedging using q-forwards or longevity bonds reduces the longevity risk substantially for life annuities, but significantly less for deferred annuities. For inflation-indexed annuities, static hedging of longevity is less effective because of the inflation risk. Variable annuities provide limited longevity protection compared to life annuities and indexed annuities, and as a result longevity risk hedging adds little value for these products.