Transient results for a high demand CCRC model

Abstract

This paper examines the transient behavior of a stochastic model for high demand continuing care retirement community (CCRC) populations. The CCRC under consideration provides a number of independent living units each of which houses one resident at a time and a skilled nursing facility (SNF) for those who require care. A time-homogeneous Markov process is used to model the care requirements of the CCRC residents. Under the model, the “state” of the population is described by the number of permanent transfers and the number of temporary transfers to the SNF. The paper examines how one can obtain information about the distribution of the state of the CCRC population at a given future time.     

Methods for the Analysis of CCRC Data

Abstract

This paper presents an approach to analyzing continuing care retirement community (CCRC) data and demonstrates the methodology by using data from a CCRC. It is assumed that residents make "transitions" among a number of "states" that represent the levels of care required by residents. There is randomness associated with both the transition times and the states entered at these times. The model is conveniently characterized in terms of “transition intensity functions,” which represent the instantaneous rates of transition between pairs of states. Statistical methods for estimating these functions are discussed, and estimates are obtained from the data-set. A simulation approach for determining probabilities and other interesting quantities based on the estimated intensity functions is also described and illustrated.     

中国长期护理保险财政负担能力研究

本文通过测算城乡居民和城镇职工长期护理保险需求,构建医疗保险精算模型,对中国长期护理保险财政负担能力展开研究。结果发现:依托城乡居民医疗保险建立的长期护理保险会增加财政支出,但是支出规模在可控范围内;依托城镇职工医疗保险建立的长期护理保险会威胁职工医疗保险统筹基金的安全,因而不可持续,但是该问题可以通过改革职工医疗保险个人账户来解决;中国长期护理保险应该采用“个人缴费+医疗保险基金补助+财政补助”的模式,且个人缴费最高不超过15%;中国长期护理保险财政负担水平总体较低,财政有能力维持长期护理保险的运行。对此,我国应尽快正式建立全国性的长期护理保险制度和财政对长期护理保险的投入机制。     

Measuring Terminable Postretirement Obligations

Abstract

New approaches are needed to value benefit plans subject to unilateral changes or termination. The paper focuses on postretirement health benefits, but the thesis may be relevant to any flow not guaranteed by law or accumulating funds.

Retiree health benefits have usually been extended to participating active employees only in concert with a reserved right by the plan sponsor to control the design and, by implication, the cash flow. Over the course of the last fifteen years, this reserved extension of benefits has almost invariably led to reductions in benefits, when compared to the plan of benefits at an earlier period. In most cases, such reductions were anticipated under the circumstances that came to prevail (high health care cost increases), but were not taken into account by most of the projection and discounting methods of the time.

Current actuarial and accounting methods generate present values for terminable retiree health plans that have little credibility as measures of the beneficiary’s asset or the sponsor’s liability. Improvements are needed that will expand the actuarial toolbox and provide solutions to economic and accounting problems.

This paper provides a basis for discussion of assumptions that are appropriate when the plan sponsor can unilaterally and dramatically change future cash flows. The paper discusses how actuaries might best approach measurement situations where further plan reductions, or outright terminations, are to be anticipated. It introduces refinements and briefly discusses how each would fit with the usual actuarial model and how differences might affect behavior. These ideas are related to financial economics and the Bader-Gold paper “Reinventing Pension Actuarial Science.” Before concluding, the wider topic of discount rate selection is briefly addressed.     

How Does Infrastructure Construction Affect Economic Development along the “Belt and Road”: By Promoting Growth or Improving Distribution?

ABSTRACT

The “Belt and Road Initiative” has involved deepening infrastructure construction along the “Belt and Road”. Using data from countries who have joined the “Belt and Road”, this study examines how infrastructure construction has affected economic development along the route. Findings show that infrastructure construction can promote economic growth and per capita output growth while improving income distribution of residents along the “Belt and Road”. Results also indicate that the effect of infrastructure construction on economic development is heterogeneous; such construction can substantially increase economic growth in developing countries but has no significant effect on economic growth in developed and emerging developing countries. Infrastructure construction can greatly improve residents’ income distribution in developed and developing countries but has no significant effect on residents in emerging developing countries. Collectively, these findings identify foreign direct investment and urbanization as important channels through which infrastructure construction can influence economic development.     

Interval Estimation of Actuarial Risk Measures

Abstract

This article investigates performance of interval estimators of various actuarial risk measures. We consider the following risk measures: proportional hazards transform (PHT), Wang transform (WT), value-at-risk (VaR), and conditional tail expectation (CTE). Confidence intervals for these measures are constructed by applying nonparametric approaches (empirical and bootstrap), the strict parametric approach (based on the maximum likelihood estimators), and robust parametric procedures (based on trimmed means).

Using Monte Carlo simulations, we compare the average lengths and proportions of coverage (of the true measure) of the intervals under two data-generating scenarios: “clean” data and “contaminated” data. In the “clean” case, data sets are generated by the following (similar shape) parametric families: exponential, Pareto, and lognormal. Parameters of these distributions are selected so that all three families are equally risky with respect to a fixed risk measure. In the “contaminated” case, the “clean” data sets from these distributions are mixed with a small fraction of unusual observations (outliers). It is found that approximate knowledge of the underlying distribution combined with a sufficiently robust estimator (designed for that distribution) yields intervals with satisfactory performance under both scenarios.     

Some Nonlinear Threshold Autoregressive Time Series Models for Actuarial Use

Abstract

This paper introduces nonlinear threshold time series modeling techniques that actuaries can use in pricing insurance products, analyzing the results of experience studies, and forecasting actuarial assumptions. Basic “self-exciting” threshold autoregressive (SETAR) models, as well as heteroscedastic and multivariate SETAR processes, are discussed. Modeling techniques for each class of models are illustrated through actuarial examples. The methods that are described in this paper have the advantage of being direct and transparent. The sequential and iterative steps of tentative specification, estimation, and diagnostic checking parallel those of the orthodox Box-Jenkins approach for univariate time series analysis.     

Insurance premiums and default risk in mutual insurance

Abstract

Two types of default risk are discussed in the article: The traditional “probability of ruin” (insurer being unable to meet his obligations) and a “perceived probability of ruin” (the probability of the insured being affected by ruin). The explicit relationship between these probabilities on the actuarial loading factors of a mutual insurer were developed. The explicit mathematical formulae obtained for these complex relationships were followed also by numerical results. A second concept presented in the paper is related to the idea of actuarially fair premiums. It is shown that the premium must also be a function of the payments of the other insured as well as their claim distributions, reflecting thereby the simultaneity and mutual dependence of the insured.     

The estimation of mortality and other decremental probabilities

Abstract

The standard actuarial methods of estimating the age-specific one-year probabilities of death in a given community were developed—for the most part, many years ago-with large bodies of observations in mind. Although the familiar “exposed to risk” procedure is known to provide unbiased estimates only when a rather dubious assumption is made about the progression of the instantaneous death-rate (the force of mortality) over the year of age (Cantelli, 1914) it is still the most widely used method of estimation. This is partly because the age-to-age increment in human mortality is relatively small—so that assumptions about its mathematical form are unimportant—and partly because suggested methods of estimation based on more “realistic” assumptions are usually laborious to apply to thousands of observations.     

Impacts on Economic Security Programs of Rapidly Shifting Demographics

Abstract

This paper analyzes in some detail potential impacts on economic security programs—government, employer, and individual—that the aging of the baby boom generation may create. It begins by defining what is meant by “population aging” and concludes that fertility shifts are more important than improving life expectancy. It also argues that calling the baby boom the “postwar baby boom” is inaccurate and will lead to missed targets for product development and marketing. Finally, this section of the paper notes that the most rapidly growing segment of the population will be the oldest old—those age 85 and over, who will also put the greatest stress on the provision of health care and retirement income security.

The paper then looks at other demographic shifts of importance, in particular female labor force participation rates. The impact of shifting demographics is reviewed for each sponsor of economic security programs: the government (health care and social security); the employer (pension plans and group benefits); and the individual. Points of concern and offsetting opportunities for the insurance industry are noted. Finally, the paper looks at whether we will be able to “afford” the sudden retirement of the baby boom. The conclusion is that this will be affordable if we can convince a portion of the labor force to stay active longer, and if we have healthy productivity growth rates. The problems of an aging population can all be viewed as opportunities for those who have the map.     

Implementation of Four Models for Outstanding Liabilities in Winbugs: A Discussion of a Paper by Ntzoufras and Dellaportas

Abstract

Ntzoufras and Dellaportas (2002) described four models for outstanding claim amounts of the “reported but not settled” variety. Two of the models incorporated claim-counts data in addition to the claim amounts themselves in order to add a hierarchical stage in the usual log-normal and state-space models. The purpose of this discussion is to describe how the models presented in Ntzoufras and Dellaportas may be implemented using WinBUGS. The use of WinBUGS to implement the Bayesian analysis of a number of other actuarial models was considered by Scollnik (2001).     

Market Value Of Insurance Liabilities

Abstract

With Statement of Financial Accounting Standards 115 (FASB 1993), insurers are now in the awkward situation that almost half of the balance sheet is marked to market. This has created a material inconsistency with the way liabilities are reported, thus diminishing the usefulness of financial reporting to shareholders and potential new investors. Discussion has emerged in the industry about the process of market valuing liabilities. The American Academy of Actuaries has formed a “Fair Valuation of Liabilities” task force to compare and review various alternative methodologies. During 1995 the Society of Actuaries and New York University jointly sponsored a conference on “Fair Value of Insurance Liabilities.” Motivated by the conference, this paper attempts to bridge the gap between option pricing and actuarial appraisal methodologies. The author suggests we refocus attention toward the assumption-setting process, which is the key driver of a fair valuation. In this regard, this paper attempts to advance practice and methodology with respect to life insurance company valuation.     

Patterns of Aging-Related Changes on the Way to 100

Abstract

The objective of this paper is to investigate dynamic properties of age trajectories of physiological indices and their effects on mortality risk and longevity using longitudinal data on more than 5,000 individuals collected in biennial examinations of the Framingham Heart Study (FHS) original cohort during about 50 subsequent years of follow-up. We first performed empirical analyses of the FHS longitudinal data. We evaluated average age trajectories of indices describing physiological states for different groups of individuals and established their connections with mortality risk. These indices include body mass index, diastolic blood pressure, pulse pressure, pulse rate, level of blood glucose, hematocrit, and serum cholesterol. To be able to investigate dynamic mechanisms responsible for changes in the aging human organisms using available longitudinal data, we further developed a stochastic process model of human mortality and aging, by including in it the notions of “physiological norms,” “allostatic adaptation and allostatic load,” “stress resistance,” and other characteristics associated with the internal process of aging and the effects of external disturbances. In this model, the persistent deviation of physiological indices from their normal values contributes to an increase in morbidity and mortality risks. We used the stochastic process model in the statistical analyses of longitudinal FHS data. We found that different indices have different average age patterns and different dynamic properties. We also found that age trajectories of long-lived individuals differ from those of the shorter-lived members of the FHS original cohort for both sexes. Using methods of statistical modeling, we evaluated “normal” age trajectories of physiological indices and the dynamic effects of allostatic adaptation. The model allows for evaluating average patterns of aging-related decline in stress resistance. This effect is captured by the narrowing of the U-shaped mortality risk (considered a function of physiological state) with age. We showed that individual indices and their rates of change with age, as well as other measures of individual variability, manifested during the life course are important contributors to mortality risks. The advantages and limitations of the approach are discussed.     

A Model for Analyzing the Impact of Selective Lapsation on Mortality

Abstract

This paper presents a model for examining the effect of various relationships between mortality rates and lapse rates on the mortality experience of a cohort of insured lives. The approach is individual rather than the aggregate traditionally used in analyzing selective lapsation. The model assumes that insured lives are healthy at policy issue, but later may move to an impaired state from which the lapse rate is zero. Associated with each insured is an unobservable “risk level” random variable, which reflects the heterogeneity of the insured group. Individual mortality and lapse rates are functions of the risk level. A numerical illustration provides some interesting results obtained by using this model.     

Factors Affecting Retirement Mortality

Abstract

As many countries consider mandatory individual retirement accounts as their answer to a secure social security system, the question arises as to whether all workers can get true “market value” annuities when they retire. It is clear today that private-sector life annuities are priced assuming that the applicant is healthy—very healthy. Very little underwriting or risk classification now exists in the individual annuity marketplace. However, if a large percentage of the population were looking to annuitize their social security accounts upon retirement, there would be strong pressure for more risk classes in the annuity-pricing structure.

Even without the advent of individual accounts for social security, the authors of this paper feel there may be real market opportunities for more risk classification in the individual annuity market and the offering of “impaired life annuities.” Given that this pressure does or might soon exist, this paper reviews 45 recent research papers that look at factors that affect mortality after retirement. In particular, factors that seem to be important in predicting retirement mortality include age, gender, race and ethnicity, education, income, occupation, marital status, religion, health behaviors, smoking, alcohol, and obesity. for each factor, this paper gives highlights relative to the named factor of the impact expected from that variable as described in the 45 reviewed research papers.

The authors believe there is a wealth of information contained in the summaries that follow, and it is our sincere hope that this paper will cause an increased interest in a more broadly based risk classification structure for individual annuities.

Summaries of the 45 papers can be found at www.soa.org/sections/farm/farm.html.     

Immediate Annuity Pricing in the Presence of Unobserved Heterogeneity

Abstract

One of the acknowledged difficulties with pricing immediate annuities is that underwriting the annuitantis life is the exception rather than the rule. In the absence of underwriting, the price paid for a life-contingent annuity is the same for all sales at a given age. This exposes the market (insurance company and potential policyholder alike) to antiselection. The insurance company worries that only the healthiest people choose a life-contingent annuity and therefore adjust mortality accordingly. The potential policyholders worry that they are not being compensated for their relatively poor health and choose not to purchase what would otherwise be a very beneficial product.

This paper develops a model of underlying, unobserved health. Health is a state variable that follows a first-order Markov process. An individual reaches the state “death” either by accident from any health state or by progressively declining health state. Health state is one-dimensional, in the sense that health can either “improve” or “deteriorate” by moving farther from or close to the “death” state, respectively. The probability of death in a given year is a function of health state, not of age. Therefore, in this model a person is exactly as old as he or she feels.

I first demonstrate that a multistate, ageless Markov model can match the mortality patterns in the common annuity mortality tables. The model is extended to consider several types of mortality improvements: permanent through decreasing probability of deteriorating health, temporary through improved distribution of initial health state, and plateau through the effects of past health improvements.

I then construct an economic model of optimal policyholder behavior, assuming that the policyholder either knows his or her health state or has some limited information. the value of mortality risk transfer through purchasing a life-contingent annuity is estimated for each health state under various risk-aversion parameters. Given the economic model for optimal purchasing of annuities, the value of underwriting (limited information about policyholder health state) is demonstrated.     

The Evolution of the Belt and Road Trade Network and Its Determinant Factors

ABSTRACT

This study reveals the evolution of the Belt and Road trade network, and discusses the determinant factors of trade relationships by employing network analysis methods. Using 65 countries’ trade flow data in 2012, 2014, and 2016, the network indices show that the Belt and Road initiative has improved trade network’s connectivity significantly. The results of blockmodels show that the trade network can be partitioned into four blocks, including “Dominators,” “Brokers,” “Generators,” and “Receivers.” Furthermore, the spatial proximity, cultural differences, trade agreements, economic distance, and trade facilitations have significant impacts on the formation of trade network according to the QAP model.     

Fuzzy Financial Pricing of Property-Liability Insurance

Abstract

This paper uses fuzzy set theory (FST) to solve a problem in actuarial science, the financial pricing of property-liability insurance contracts. The fundamental concept of FST is the alternative formalization of membership in a set to include the degree or strength of membership. FST provides consistent mathematical rules for incorporating vague, subjective, or judgmental information into complex decision processes. It is potentially important in insurance pricing because much of the information about cash flows, future economic conditions, risk premiums, and other factors affecting the pricing decision is subjective and thus difficult to quantify by using conventional methods. To illustrate the use of FST, we “fuzzify” a well-known insurance financial pricing model, provide numerical examples of fuzzy pricing, and propose rules for project decision-making using FST. The results indicate that FST can lead to significantly different decisions than the conventional approach.     

Financial Economics and Actuarial Practice

Abstract

Starting in the United Kingdom and continuing through the U.S. and Canadian actuarial professions, proponents of financial economics have been forcefully promoting a review of traditional actuarial practices and training. In particular, the financial theories first proposed by Modigliani and Miller and subsequently developed by others have been used to highlight serious weaknesses in typical actuarial thinking. In summary, it is claimed that much actuarial advice wrongly specifies value, that guidelines and standards need radical revision, and that traditional actuarial intuition suffers in comparison to newer modes of thought adopted by other professions.

This paper examines concepts from both financial economics and actuarial science as applied to defined benefit schemes using a simple discounted cash-flow framework as a reference point. The general finding is that many standard modes of actuarial thought are, in fact, indefensible when examined with the tools and techniques of financial economics. The call for revision of actuarial training and practices is credible and necessary.

However, the paper also touches upon areas where a heavy-handed application of finance theory could be misguided due to limitations in the simple financial economic models presented. It concludes that financial economics should be carefully integrated into actuarial thought rather than appended to existing actuarial theory or inserted as a wholesale replacement.     

Credibility Using Copulas

Abstract

Credibility is a form of insurance pricing that is widely used, particularly in North America. The theory of credibility has been called a “cornerstone” in the field of actuarial science. Students of the North American actuarial bodies also study loss distributions, the process of statistical inference of relating a set of data to a theoretical (loss) distribution. In this work, we develop a direct link between credibility and loss distributions through the notion of a copula, a tool for understanding relationships among multivariate outcomes.

This paper develops credibility using a longitudinal data framework. In a longitudinal data framework, one might encounter data from a cross section of risk classes (towns) with a history of insurance claims available for each risk class. For the marginal claims distributions, we use generalized linear models, an extension of linear regression that also encompasses Weibull and Gamma regressions. Copulas are used to model the dependencies over time; specifically, this paper is the first to propose using a t-copula in the context of generalized linear models. The t-copula is the copula associated with the multivariate t-distribution; like the univariate tdistributions, it seems especially suitable for empirical work. Moreover, we show that the t-copula gives rise to easily computable predictive distributions that we use to generate credibility predictors. Like Bayesian methods, our copula credibility prediction methods allow us to provide an entire distribution of predicted claims, not just a point prediction.

We present an illustrative example of Massachusetts automobile claims, and compare our new credibility estimates with those currently existing in the literature.