Knowledge Elicitation of Gompertz' Law of Mortality

A new formulation of Gompertz' law of mortality is proposed. Explicit formulas for moment generating function and moments of this formulation are derived. The new formulation is applied to the theory of heterogeneous populations and formulas for stop-loss transformations are derived.     

Research Into the Aging Process: A Survey

Abstract

We are in the midst of a revolution in biological knowledge. Although research into the aging process was begun long before the Human Genome Project, it has benefited greatly from the powerful tools and techniques spun off from that endeavor. Current research is providing knowledge about life processes that may offer the prospect of slowing the aging process. Dr. Francis Collins, Director of the National Human Genome Research Institute, has predicted that “By 2030, major genes responsible for the aging process in humans will likely have been identified, and clinical trials with drugs to retard the process may well be getting underway” (Collins 2000). A growing number of scientists recognize extension of the maximum life span as a possibility.

The actuarial profession cannot lay claim to expertise in the area of mortality while ignoring scientific research into the causes of aging. This paper provides a brief overview of the subject and a bibliography for those interested in pursuing the matter further. It offers a brief historical perspective, a survey of current research, and a glimpse of future possibilities.?     

Killing the Law of Large Numbers: Mortality Risk Premiums and the Sharpe Ratio

We provide an overview of how the law of large numbers breaks down when pricing life‐contingent claims under stochastic as opposed to deterministic mortality (probability, hazard) rates. In a stylized situation, we derive the limiting per‐policy risk and show that it goes to a non‐zero constant. This is in contrast to the classical situation when the underlying mortality decrements are known with certainty, per policy risk goes to zero. We decompose the standard deviation per policy into systematic and non‐systematic components, akin to the analysis of individual stock (equity) risk in a Markowitz portfolio framework. Finally, we draw upon the financial analogy of the Sharpe Ratio to develop a premium pricing methodology under aggregate mortality risk.     

On the Moments of the Time of Ruin with Applications to Phase-Type Claims

Abstract

We describe an approach to the evaluation of the moments of the time of ruin in the classical Poisson risk model. The methodology employed involves the expression of these moments in terms of linear combinations of convolutions involving compound negative binomial distributions. We then adapt the results for use in the practically important case involving phase-type claim size distributions. We present numerical examples to illuminate the influence of claim size variability on the moments of the time of ruin.     

上海市人口老龄化与养老服务体系建设

21世纪上半叶,上海市户籍老年人养老服务需求增长速度将明显在快于老年人口数增长速度。本文在概括近年来上海市按＂9073＂养老服务格局要求加快养老服务体系建设的基础上,提出了相应对策和建议,认为上海市应按适度比例增加养老机构床位数,完善养老服务优惠政策,加强对亲属或民间保姆照顾的支持,重视老年人心灵关爱等,更进一步地搞好养老服务体系的建设。     

商业银行流程再造与总法律顾问制度的构建

任何一次规模巨大的金融危机,都是对金融体系脆弱环节的集中暴露,同时已为银行业反思与改进提供了机遇.许多国际大银行公开承认,危机之前奉行的发展战略及与之相应的流程设计存在明显缺陷,并先后开展战略反思和流程再造,基于对危机以来法律风险的重新认识,积极创新法律风险管理机制,相继建立起总法律顾问制度.当前,我国商业银行的法律风险已延伸到每一个业务条线下,总法律顾问制度应成为商业银行决策和风险管理机制的重要组成部分.本文归纳总结了后危机时代国际大银行对流程再造与总法律顾问几个问题的重新认识,阐述了总法律顾问制度在商业银行流程再造中发挥的重要作用,提出了构建我国商业银行总法律顾问制度的建议.     

Mortality Regimes and Pricing

Abstract

Mortality dynamics are characterized by changes in mortality regimes. This paper describes a Markov regime-switching model that incorporates mortality state switches into mortality dynamics. Using the 1901-2005 U.S. population mortality data, we illustrate that regime-switching models can perform better than well-known models in the literature. Furthermore, we extend the 1992 Lee-Carter model in such a way that the time-series common risk factor to all cohorts has distinct mortality regimes with different means and volatilities. Finally, we show how to price mortality securities with this model.     

Mortality Change and Forecasting

Abstract

Prospects of longer life are viewed as a positive change for individuals and as a substantial social achievement but have led to concern over their implications for public spending on old-age support. This paper makes a critical assessment of knowledge about mortality change. It is oriented toward the problem of forecasting the course of mortality change and the potential of existing work to contribute to the development of useful forecasts in Canada, Mexico, and the U.S.

We first examine broad patterns in the historical decline in death rates in the three countries, the effect of these on trends in life expectancy, and the epidemiological transition. Next we review theories of the age pattern and evolution of mortality, including graduations, evolutionary theory, reliability models, dynamic models, and relational models.

The analysis and forecasting of mortality change have been shaped largely by some key historical lessons, which we summarize next. We emphasize issues that have been or are likely to be significant in mortality analysis, especially the questions of the age pattern and time trend in mortality at old ages; we distinguish patterns and facts that are established from those that remain uncertain. Next, we consider mortality differentials in characteristics such as sex, marital status, education, and socioeconomic variables; we summarize their key features and also point to the substantial gaps in our understanding of their determinants.

Finally, we review methods of forecasting, including the scenario method used by the U.S. Social Security Administration and the time series method of Lee and Carter. We set out some important recommendations for forecasters: forecasting assumptions should be made more formal and explicit; there should be retrospective evaluations of forecast performance; and greater attention should be paid to the assessment and consequences of forecast uncertainty.     

Purged and partial Markov chains

Abstract

In multiple decrement theory, disability theory, nuptiality and fertility theory, and in other connections, actuaries and demographers often study what in effect is simple Markov chain models. In these models, the transition probabilities, are defined on the basis of the forces of transition (infinitesimal transition probabilities). For various reasons, new models are sometimes constructed by replacing some of the original forces of transition by 0. We shall call the transition probabilities of such a new model partial probabilities.     

Systematic Mortality Improvement Trends and Mortality Heterogeneity: Insights from Individual-Level HRS Data

Providers of life annuities and pensions need to consider both systematic mortality improvement trends and mortality heterogeneity. Although how mortality improvement varies with age and gender at the population level is well studied, how trends vary with risk factors remains relatively unexplored. This article assesses how systematic mortality improvement trends vary with individual risk characteristics using individual-level longitudinal data from the U.S. Health and Retirement Study between 1994 and 2009. Initially a Lee-Carter model is used to assess mortality improvement trends by grouping individuals with similar risk characteristics of gender, education, and race. We then fit a longitudinal mortality model to individual-level data allowing for heterogeneity and time trends in individual-level risk factors. Our results show how survey data can provide valuable insights into both mortality heterogeneity and improvement trends more effectively than commonly used aggregate models. We show how mortality improvement differs across individuals with different risk factors. Significantly, at an individual level, mortality improvement trends have been driven by changes in health history such as high blood pressure, cancer, and heart problems rather than risk factors such as education, marital status, body mass index, and smoker status.     

不同组织形式下私募股权投资基金运作过程中的法律适用规则

法律有规范,做事有规则。在当今的法制社会里,任何一种民事、经济活动都有法律规范的约束及法律规则的适用,私募股权投资基金也是如此。到目前为止,虽然我国还没有颁布专门的针对私募股权投资基金行为的立法,但私募股权投资基金的四种组织形式都有现成的相对应的法律规范存在,研究这四种组织形式的业务流程,把握法律规则在私募股权投资基金组织形式中的适用,是降低投资者投资风险,减少投资纠纷的重要一环。     

老龄化与日本的社会保障

日本今年3月发生的大地震和核发电站的泄露事故,给政府和国民敲响警钟,震灾后的复兴,同时也是日本社会保障、社会福利的复兴。本文就日本的老龄化、社会保障、社会福利服务的现状进行分析,同时提出了社会保障构造改革后社会保障政策的诸多问题,并就日本社会保障未来的发展方向提出了思考和建议。     

Measuring Corporate Bond Mortality and Performance

This study develops an alternative way to measure default risk and suggests an appropriate method to assess the performance of fixed-income investors over the entire spectrum of credit-quality classes. The approach seeks to measure the expected mortality of bonds and the consequent loss rates in a manner similar to the way actuaries assess mortality of human beings. The results show that all bond ratings outperform riskless Treasuries over a ten-year horizon and that, despite relatively high mortality rates, B-rated and CCC-rated securities outperform all other rating categories for the first four years after issuance, with BB-rated securities outperforming all others thereafter.     

On the Modeling and Forecasting of Socioeconomic Mortality Differentials: An Application to Deprivation and Mortality in England

In any country, mortality rates and indices such as life expectancy usually differ across subpopulations, for example, defined by gender, geographic area, or socioeconomic variables (e.g., occupation, level of education, or income). These differentials, and in particular those related to socioeconomic circumstances, pose important challenges for the design of public policies for tackling social inequalities, as well as for the design of pension systems and the management of longevity risk in pension funds and annuity portfolios. We discuss the suitability for the modeling and forecasting of socioeconomic differences in mortality of several multiple population extensions of the Lee-Carter model, including a newly introduced relative model based on the modeling of the mortality in socioeconomic subpopulations alongside the mortality of a reference population. Using England mortality data for socioeconomic subpopulations defined using a deprivation index, we show that this new relative model exhibits the best results in terms of goodness of fit and ex post forecasting performance. We then use this model to derive projections of deprivation specific mortality rates and life expectancies at pensioner ages and analyze the impact of socioeconomic differences in mortality on the valuation of annuities.     

Credit rating dynamics and Markov mixture models

Despite mounting evidence to the contrary, credit migration matrices, used in many credit risk and pricing applications, are typically assumed to be generated by a simple Markov process. Based on empirical evidence, we propose a parsimonious model that is a mixture of (two) Markov chains, where the mixing is on the speed of movement among credit ratings. We estimate this model using credit rating histories and show that the mixture model statistically dominates the simple Markov model and that the differences between two models can be economically meaningful. The non-Markov property of our model implies that the future distribution of a firm’s ratings depends not only on its current rating but also on its past rating history. Indeed we find that two firms with identical current credit ratings can have substantially different transition probability vectors. We also find that conditioning on the state of the business cycle or industry group does not remove the heterogeneity with respect to the rate of movement. We go on to compare the performance of mixture and Markov chain using out-of-sample predictions.     

Population Aging and International Monetary Transmission

This paper examines whether U.S. monetary policy has different effects on young and old countries. I first empirically show that a contractionary U.S. monetary policy shock brings about a smaller fall in output and a greater rise in net exports in old countries using vector autoregressions (VARs), and that the shock leads to a larger fall in consumption and a smaller decrease in investment in old countries using the local projection method. I then construct a three-country life-cycle model including the U.S., a young country, and an old country. Consistent with the empirical analyses, the simulation results of the model show that a contractionary U.S. monetary policy shock has weaker effects on output in the old country than in the young country. In response to the shock, despite a larger fall in consumption in the old country, investment there decreases by less and net exports rise by more, which enables output in the old country to decline by less. The stronger incentives to save in the old country, resulting from the longer life expectancy and hence the longer retirement period, play a key role in generating these results.     

人口老龄化与劳动力成本粘性

本文以2005-2017年中国A股上市公司为研究样本,采用我国各个省份的常住人口老龄化数据衡量人口老龄化程度,实证检验了人口老龄化对于企业劳动力成本粘性的影响。结果表明,人口老龄化显著提高劳动力成本粘性。进一步研究发现,人口老龄化对劳动力成本粘性的影响在劳动密集型企业和民营企业中更加显著。本文从企业微观视角出发,考察人口老龄化对企业人力成本的影响,加深了我们对人口老龄化经济后果的认识。本文结果表明推动企业优化升级是降低人口老龄化负面影响的重要途径。     

Markov Chains and Regression toward the Mean

Using the theory of stationary Markov chains, we uncover a previously unknown property of the behavior of betas. Specifically, if the cross-sectional distribution of betas is stationary over time, then the set of firms that remain in an arbitrarily chosen beta interval between one period and the next will not regress toward the mean. This surprising result occurs in spite of the well-known fact that the set of all the firms in the interval will exhibit the regression tendency. Our empirical tests indicate that betas behave in remarkable accordance with this prediction.     

On stationary point processes and Markov chains

Abstract

Introductory. In the theory of random processes we may distinguish between ordinary processes and point processes. The former are concerned with a quantity, say x (t), which varies with time t, the latter with events, incidences, which may be represented as points along the time axis. For both categories, the stationary process is of great importance, i. e., the special case in which the probability structure is independent of absolute time. Several examples of stationary processes of the ordinary type have been examined in detail (see e. g. H. Wold 1). The literature on stationary point processes, on the other hand, has exclusively been concerned with the two simplest cases, viz. the Poisson process and the slightly more general process arising in renewal theory (see e. g. J. Doob 3).     

Mortality of Smoking by Gender

Exposure to cigarette smoke has had and will continue to have a huge effect on mortality. Significant differences in smoking prevalence rates by gender have contributed to varying levels and rates of improvement in mortality over the last several decades and are expected to continue to influence mortality improvement differently over the next several decades. The combined effect of greater historical smoking prevalence rates by males and their corresponding earlier and larger reduction has in part been responsible for the recent improvement in mortality rates for males compared to that for females in the United States. Similar patterns are evident in almost all economically developed countries, although their timing and levels differ. The patterns in less-developed countries will likely follow similar patterns as concerns emerge about the effect of smoking on the mortality of their citizens. The objective of this article is to compare smoking prevalence and cessation by gender and the effect on smoking-attributable and, in turn, all-cause mortality. A summary of mortality attribution approaches used to enhance the evaluation of the effect of smoking and projections of mortality rates by gender is also provided.