基于长寿背景下的企业年金风险评估

在死亡率不断降低,预期寿命不断提高的背景下,企业年金实现一定替代率目标的难度不断增大,面临的长寿风险越来越不容忽视。在中国人口死亡率最优模型基础上,通过企业年金比率模型评估了三种不同年龄结构企业年金的长寿风险,并在基于Bootstrap方法的VAR模型上考虑了投资风险,对企业年金进行综合风险分析。结果表明,当其他风险都能被完全对冲时,未来死亡率降低及预期寿命延长会对企业年金实现目标养老待遇产生较大影响,并且评估期越长,企业年金积累的长寿风险越大。     

有限数据下Lee-Carter模型在人口死亡率预测中的应用

Lee-Carter模型是当今世界上最流行的死亡率建模与预测模型,传统的Lee-Carter模型在样本量很大时才能得到较好的效果,而中国的死亡率数据量较少,且部分年限的数据缺失,从而难以达到较好的预测效果。本文基于Li等(2004)提出的有限数据死亡率建模方法,同时考虑样本量不足的影响,采用韩猛等(2010)提出的“双随机过程”建模,构建了有限数据下中国人口死亡率的预测模型,并用于对未来死亡率变动趋势和人口寿命的预测,最后将预测结果与保险公司采用的死亡率改善因子以及社会养老保险个人账户中采用的计发月数进行对比分析,给出了若干相关结论和有关死亡率风险管理的建议。     

基于分位自回归的中国人口死亡率动态预测

采用1994-2012年国家统计局公布的死亡率数据,针对Lee-Carter模型的预测方法提出改进,将分位自回归方法内置到Lee-Carter模型框架中,构建中国人口死亡率的分位自回归预测模型,对未来人口死亡率的变动趋势进行预测。通过与传统的均值回归方法比较,得出结论为:人口死亡率的分位自回归预测方法能够获取更加全面的信息,能够有效应对人类预期寿命被低估的可能,从而对未来死亡率的预测更加合理、可信。     

我国人口死亡风险异质与混合模型研究

多人口随机死亡率模型是人口统计和保险精算领域的前沿问题。建立符合我国人口特征的死亡率预测模型，对人口预测、长寿风险度量和积极管理长寿风险具有重要意义。然而，当前研究中对人口死亡风险异质性问题的关注较少，不能为多人口随机死亡率建模提供科学的研究假设。本文从我国人口死亡风险异质性的检验出发，构建两性别人口死亡率联合预测的混合泊松公因子模型，并给出极大似然参数估计的迭代算法，对我国男女两性别人口死亡率进行联合建模和预测，最后用于对保险公司养老年金的长寿风险资本需求测算。研究表明，混合泊松公因子模型能够有效刻画人口死亡风险的异质性，提升模型拟合优度，有效避免传统模型低估人口死亡率改善的弊端，并且死亡率性别比变动趋势符合人类生物规律。在风险导向的第二代偿付能力体系下，本文提出的死亡率模型能够为保险公司提供更稳健的长寿风险资本评估。     

死亡率预测模型的新进展

近半个世纪以来,世界范围内,人口死亡率整体上呈现下降趋势。而依据传统死亡模型对死亡率的预测往往高于实际水平,这给养老金财务安排和养老年金的成本核算带来了严重的不利影响。本文沿着死亡率模型的发展轨迹,回顾和总结了各类死亡率预测模型,对死亡率预测模型的最新进展做出评述,并对中国死亡率预测模型的选取给出了建议。     

函数型死亡率预测模型

人口死亡率反映人口的死亡水平,是人口规模的重要影响因素,同时也是人寿保险精算的重要数据基础。从数据特征来看,死亡率作为年龄的函数,是一种典型的函数型数据。本文使用函数型数据方法分析中国人口数据,基于1994—2010年中国人口分年龄死亡数据,建立函数型死亡率预测模型,对未来分年龄死亡率进行预测,并通过生命表方法计算了未来平均预期寿命。同时通过对历史数据的预测,说明模型预测结果比较可信。     

中国高龄人口死亡率随机波动趋势分析

本文采用1996-2010年国家统计局公布的死亡率数据,以70岁男性人口作为高龄人口的代表,基于中国人口死亡率数据较少的特点,突破了传统Lee-Carter模型的框架,直接从死亡率改善产生的原因入手,采取Monte Carlo方法建立中国高龄人口死亡率随机波动趋势模型。通过对不同死亡率改善原因进行组合,从中选取最优模型来探究死亡率的随机趋势性与波动性的关系,更好的克服了死亡率普遍被低估的事实,使得对未来死亡率的预测更加准确与稳妥。     

我国男女两性老龄人口死亡率联合建模与预测

老龄人口死亡率建模和预测是长寿风险度量和养老金风险管理的基础。在我国,退休年龄及以上老龄人口死亡数据稀少,随机波动大,构建能够捕捉老龄人口死亡率随性别、年龄和时间变动的动态预测模型成为难题。本文采用Logistic两人口死亡率模型研究我国老龄人口死亡率的建模与预测。首先,运用死亡率数据质量较好的我国台湾地区数据,对模型结构进行选择,并检验模型的稳健性和预测性能。其次,基于我国大陆地区死亡率数据对模型结构进行二次验证和选择,应用所选模型对大 陆地区老龄死亡率进行建模和预测。结果显示,对于我国男女老龄死亡率的拟合和预测,Logistic 两人口模型均优于单人口CBD模型。最后,运用Logistic两人口死亡率模型对死亡率在年龄和时间两个维度上外推和预测,计算出时期和队列老龄人口分年龄的预期余寿,为养老金精算评估和长寿风险分析提供更准确的数据支持。     

基于C-K模型及其改进的高高龄人口死亡率模型研究

目前,国际上关于高龄人口死亡率估计的方法主要包括经典的参数模型估计方法,如用Gompertz分布、Makeham分布拟合高龄人口的死亡率。文章将着重探究Coale-Kisker模型在高高龄人口死亡率拟合中的应用,并针对高高龄人口死亡数据足够多时,对经典的Coale-Kisker模型提出适当的改进。     

基于VaR方法的长寿风险自然对冲模型

随着死亡率的下降与预期寿命的提高,保险公司面对着不容忽视的长寿风险。基于VaR方法探讨了长寿风险管理中的自然对冲策略,然后在对中国男性人口死亡率预测的基础上,给出了保险公司自然对冲长寿风险所需的最优产品结构,并进一步考查了利率、签单年龄、缴费方式等因素对最优产品结构的影响。     

Mortality,longevity and experiments with the Lee–Carter model

The paper reviews the Lee-Carter modelling framework, illustrated with an application, and then extends the framework through the development of a wider class of generalised, parametric, non-linear models. The choice of error distribution is also generalised. These extensions permit the modelling and extrapolation of age-specific cohort effects as well as the more familiar age-specific period effects: the age-period-cohort version of the model is discussed with a worked example. The paper also provides a comparative study of simulation strategies for assessing risk in mortality rate predictions and the associated forecast estimates of life expectancy and annuity values in both period and cohort perspectives.     

Modelling excess mortality of the unemployed: choice of scale and extra-Poisson variability

"Occupational mortality and morbidity is usually studied via standardized mortality (or morbidity) ratios, with little attention to the basic fit of the implicit underlying proportional hazards model. This paper presents a case study on unemployment and mortality, based on the complete Danish male population aged 20-64 years at the 1970 census. The effect of unemployment on the age-specific mortality rate is intermediate between additive and multiplicative and was fitted well by an additive effect on the square root of the mortality. The paper discusses and illustrates whether finer stratification or random residual variation ('frailty') is to be preferred for obtaining a statistically satisfactory fit."     

Valuation of Equity-indexed Annuities with Stochastic Interest Rate and Jump Diffusion

This article considers the pricing of equity-indexed annuity (EIA). By employing the change of measure technique, we derive the closed-form solutions for the prices of both point-to-point and annual reset equity-indexed annuities. We also provide numerical results to illustrate the method and computational efficiency of our simulation scheme and the effects of various model parameters on the participation rate.     

The Risk of a Mortality Catastrophe

We develop a continuous-time model for analyzing and valuing catastrophe mortality contingent claims based on stochastic modeling of the force of mortality. We derive parameter estimates from a 105-year time series of U.S. population mortality data using a simulated maximum likelihood approach based on a particle filter. Relying on the resulting parameters, we calculate loss profiles for a representative catastrophe mortality transaction and compare them to the “official” loss profiles that are provided by the issuers to investors and rating agencies. We find that although the loss profiles are subject to great uncertainties, the official figures fall significantly below the corresponding risk statistics based on our model. In particular, we find that the annualized incidence probability of a mortality catastrophe, defined as a 15% increase in aggregated mortality probabilities, is about 1.4%—compared to about 0.1% according to the official loss profiles.     

Past and recent attempts to model mortality at all ages

"Most laws of mortality are partial in the sense that they apply only to a broad age group and not to all ages. This paper focuses on three laws of mortality that apply to all ages. Two of them were developed by the actuaries Thiele and Wittstein in the late 19th century. The third, developed by Heligman and Pollard, is of recent origin. The three laws are discussed with references to Scandinavian mortality data. The results suggest that the most recently proposed law can be used for generation of model life tables, for making population projections, simulations, and other statistical work where there is a need for a realistic model of human mortality."     

Main changes and differentiations in the health status of Poland's population with allowances for international mortality comparisons

The health status of the population of Poland is analyzed for the postwar period, with emphasis on the 1980s. Trends in mortality, and particularly in excess male mortality, are described and compared with other European countries.     

An assessment of population losses during World War II

An attempt is made to estimate losses to the population of the USSR due to World War II by projecting the probable population in 1945 based on prewar population data and comparing the projections to the actual population in 1945. The authors calculate that the country lost between 26 and 27 million people, of which some 19 million were male. These losses include direct deaths due to the fighting, indirect mortality due to wartime conditions, and losses through emigration.