Konventionelle und moderne Einschätzungsmethoden in der Lebensversicherungsmedizin

The concepts of tariffs in the life insurance are built up with several layers of models. The foundation of the risk assessment of an applicant is the mortality rate in the actuarial model, based on the selection factors of gender and age. In the conventional medical risk assessment the anomalies of the applicant will be transformed into extra mortality rates. With modern methods of evaluation, the risk factors of the applicant will be assessed with statistical practices, in relation to the average values of the insurance portfolio. The deviations built up the insurance medical adjustment factor of the actuarial mortality rate and the basis of the insurance economical classification of the applicant to a risk class or a tariff portfolio.     

Clustering technique for risk classification and prediction of claim costs in the automobile insurance industry

This paper considers the problem of predicting claim costs in the automobile insurance industry. The first stage involves classifying policy holders according to their perceived risk, followed by modelling the claim costs within each risk group. Two methods are compared for the risk classification stage: a data‐driven approach based on hierarchical clustering, and a previously published heuristic method that groups policy holders according to pre‐defined factors. Regression is used to model the expected claim costs within a risk group. A case study is presented utilizing real data, and both risk classification methods are compared according to a variety of accuracy measures. The results of the case study show the benefits of employing a data‐driven approach. © 2001 John Wiley & Sons, Ltd.     

A novel dual-weighted fuzzy proximal support vector machine with application to credit risk analysis

In this paper, a novel dual-weighted fuzzy proximal support vector machine (FPSVM) model hybridizing fuzzy set theory (FST) and proximal support vector machine (PSVM) is proposed for credit risk analysis. In the proposed model, the fuzzy memberships are introduced into both objective function and constraint conditions of PSVM model to make full use of the information of data. Due to the introduction of fuzzy set theory, the FPSVM model shows fine generalized ability and great practical value. For verification purpose, two publicly available credit datasets are used to test the effectiveness of the proposed FPSVM method. Experimental results show that the proposed FPSVM outperforms other SVM models listed in this study, indicating that the proposed FPSVM model has rather good discriminatory power and it can be used as a promising tool for other classification tasks.     

Ankle/arm blood pressure index: an insurance perspective

Recent studies conclude that the ankle/arm blood pressure index (AAI) is a useful clinical tool for refining cardiovascular risk classification in the elderly. A reduction in the AAI to 0.9 or less is associated with increased risk for both coronary heart disease and total cardiovascular disease morbidity and mortality, as well as all-cause mortality. This relationship persists after adjusting for traditional risk factors and known cardiovascular disease. AAI will appear more common in attending physician's statements, prompting a need to educate underwriters about this technology. AAI may be of particular interest to insurers dealing in the elderly market, to those with strong physician examiner systems, and in markets where blood or urine tests are not commonly used in underwriting.     

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.     

Screening potential elderly preferred markers: exploratory analysis of Cardiovascular Health Study (CHS) data

The Cardiovascular Health Study (CHS) analyzes risk factors for coronary heart disease and stroke in people age 65 and older. Since CHS is designed to comprehensively study cardiovascular risk factors in an elderly population, it provides a unique opportunity to study the association of risk factors with mortality, as well as morbidity risk. With the growth of the elderly as population and life insurance market segments, the need to more precisely stratify mortality within a standard risk group of the elderly has grown as well. This exploratory analysis assesses medical factors that could be used to improve mortality risk stratification within a "standard" mortality population, using the CHS public use data set. Participants with a personal history of cardiovascular disease, diabetes, or major electrocardiographic abnormalities were excluded from the analysis in order to mimic a standard life insurance selection process. Then, Cox proportional hazards regression was used to study 10 medical risk factors. This model suggested that forced vital capacity >80% predicted, serum creatinine <1.5 mg/dL (133 mcmol/L), hemoglobin >11 g/dL (110 g/L), and serum albumin >3.5 mg/L (35 mmol/ L) are significantly associated (p = 0.05) with favorable mortality. C-reactive protein <1 mg/L is associated with favorable mortality at borderline significance levels (p = 0.09). On the other hand, a family history of cardiovascular disease (MI and/or stroke) and low BMI (<26 kg/m2) are associated with unfavorable mortality in the analysis. Total to HDL cholesterol ratio of <6, presence of supine systolic blood pressure < or = 140 mmHg, and the presence of minor rest electrocardiographic findings were not statistically significant factors in the multivariate model. Further assessment of the predictive value of the "significant" medical factors identified is required in insured lives.     

A Fuzzy Set Approach for Generalized CRR Model: An Empirical Analysis of S&;P 500 Index Options

This paper applies fuzzy set theory to the Cox, Ross and Rubinstein (CRR) model to set up the fuzzy binomial option pricing model (OPM). The model can provide reasonable ranges of option prices, which many investors can use it for arbitrage or hedge. Because of the CRR model can provide only theoretical reference values for a generalized CRR model in this article we use fuzzy volatility and fuzzy riskless interest rate to replace the corresponding crisp values. In the fuzzy binomial OPM, investors can correct their portfolio strategy according to the right and left value of triangular fuzzy number and they can interpret the optimal difference, according to their individual risk preferences. Finally, in this study an empirical analysis of S&P 500 index options is used to find that the fuzzy binomial OPM is much closer to the reality than the generalized CRR model.This project has been supported by NSC 93-2416-H-009-024.JEL Classification:     

Beyond Age and Sex: Enhancing Annuity Pricing

This paper examines the use of more extensive risk classification and its impact on annuitisation values in consumer markets with mortality heterogeneity. Prices of U.S. retail annuities do not currently reflect buyers’ attributes other than age and sex. I qualitatively assess a number of proposed underwriting factors and show that the factors chosen can robustly predict mortality heterogeneity in a hazards framework. The relative value of annuities across demographic groups converges considerably under finer-grained pricing, but the change in consumers’ well-being is asymmetric. Shorter-lived annuitants gain about 30 per cent in financial and utility-adjusted terms, whereas longer-lived annuitants experience losses of 16 per cent.     

Individual Annuity Demand Under Aggregate Mortality Risk

Aggregate mortality risk—the risk that the mortality trend in a population changes in a nondeterministic way—and its implications for corporate decisions has recently been the subject of lively scientific discussion. We show that aggregate mortality risk is also a key determinant for individual annuitization decisions. Aggregate mortality risk appears to be a risk very difficult to transfer for individuals. Whether its existence leads to a higher or lower annuity demand depends on objective factors (e.g., insurers’ vulnerability to aggregate mortality changes). Subjective factors (i.e., individuals’ preferences) determine only the intensity of the annuity demand reaction to aggregate mortality risk. Our results are of significant importance not only for financial planning approaches of individual annuity buyers but also for strategic decisions in insurance companies and for solvency regulators. Furthermore, consideration of aggregate mortality risk may alleviate, but also intensify, the annuity puzzle.     

Cohort and value-based multi-country longevity risk management

ABSTRACT

Multi-country risk management of longevity risk provides new opportunities to hedge mortality and interest rate risks in guaranteed lifetime income streams. This requires consideration of both interest rate and mortality risks in multiple countries. For this purpose, we develop value-based longevity indexes for multiple cohorts in two different countries that take into account the major sources of risks impacting life insurance portfolios, mortality and interest rates. To construct the indexes we propose a cohort-based affine model for multi-country mortality and use an arbitrage-free multi-country Nelson–Siegel model for the dynamics of interest rates. Index-based longevity hedging strategies have the advantages of efficiency, liquidity and lower cost but introduce basis risk. Graphical risk metrics are a way to effectively capture the relationship between an insurer's portfolio and hedging strategies. We illustrate the effectiveness of using a value-based index for longevity risk management between two countries using graphical basis risk metrics. To show the impact of both interest rate and mortality risk we use Australia and the UK as domestic and foreign countries, and, to show the impact of mortality only, we use the male populations of the Netherlands and France with common interest rates and basis risk arising only from differences in mortality risks.     

Optimal Risk Classification with an Application to Substandard Annuities

Abstract

Substandard annuities pay higher pensions to individuals with impaired health and thus require special underwriting of applicants. Although such risk classification can substantially increase a company's profitability, these products are uncommon except for the well-established U.K. market. In this paper we comprehensively analyze this issue and make several contributions to the literature. First, we describe enhanced, impaired life, and care annuities, and then we discuss the underwriting process and underwriting risk related thereto. Second, we propose a theoretical model to determine the optimal profit-maximizing risk classification system for substandard annuities. Based on the model framework and for given price-demand dependencies, we formally show the effect of classification costs and costs of underwriting risk on profitability for insurers. Risk classes are distinguished by the average mortality of contained insureds, whereby mortality heterogeneity is included by means of a frailty model. Third, we discuss key aspects regarding a practical implementation of our model as well as possible market entry barriers for substandard annuity providers.     

Human Resource Allocation in a CPA Firm: A Fuzzy Set Approach

The review of existing human resource allocation models for a CPA firm shows that there are major shortcomings in the previous mathematical models. First, linear programming models cannot handle multiple objective human resource allocation problems for a CPA firm. Second, goal programming or multiple objective linear programming (MOLP) cannot deal with the organizational differentiation problems. To reduce the complexity in computing the trade-offs among multiple objectives, this paper adopts a fuzzy set approach to solve human resource allocation problems. A solution procedure is proposed to systematically identify a satisfying selection of possible staffing solutions that can reach the best compromise value for the multiple objectives and multiple constraint levels. The fuzzy solution can help the CPA firm make a realistic decision regarding its human resource allocation problems as well as the firm's overall strategic resource management when environmental factors are uncertain.     

How to prepare a life expectancy report for an attorney in a tort case

The purpose of this methodology article is to describe a suitable format for a legally acceptable report on the life expectancy of the principal in a tort case that is being advocated or defended by an attorney. Life insurance medical directors and underwriters are clearly skilled and experienced in mortality risk classification for life insurance. However, the judicial system is accustomed to measuring excess mortality only in terms of reduced life expectancy. The analyst preparing the report must convert the excess mortality into a figure for reduced life expectancy and compare this with the life expectancy of persons matched by age, sex and race in the latest Decennial US Life Tables. This process is different from the life insurance underwriting process. A life table projected to age 109 must be constructed as an essential part of the report, and the entire process must be presented clearly and convincingly. There are good reasons why the excess death rate (EDR) should be used as the index of excess mortality in constructing the life table, in preference to the mortality ratio (MR), which is used most of the time in life insurance risk classification. All of these considerations are discussed in this article, which is based on a sample of 40 cases handled by the author, a retired life insurance medical director.     

Exercise test on the older patient: is it still as predictive as for the younger patient?

Exercise testing predicts both cardiac events and mortality after age 65, just as it does for younger patients. In both age groups, functional aerobic capacity itself is a potent indicator of mortality risk. In the elderly, achievement of predicted functional aerobic capacity identifies favorable mortality even in the presence of CAD and CAD risk factors.     

A Hermite-spline model of post-retirement mortality

ABSTRACT

We present a model for post-retirement mortality where differentials automatically reduce with increasing age, but without the fitted mortality rates for subgroups crossing over. Selection effects are catered for, as are age-modulated time trends and seasonal variation in mortality. Central to the model are Hermite splines, which permit parsimonious modelling of complex risk factors in even modest-sized portfolios. The model is therefore suitable for the stand-alone analysis of experience data for reinsurance, bulk annuities and longevity swaps. We also illustrate the contrast between the statistical significance of a risk factor and its financial significance and discuss reasons why one might include risk factors like season that are not directly financially significant.     

Interaction of individual framing and political orientation in guiding climate change risk perception

There is a general agreement that climate change is a potential hazard threatening the global village. An appropriate level of risk perception should be a critical issue in coping with the global environmental risk. We examined the determinants of the level of climate change risk perception. In particular, we examined if individual framing of climate change interacts with political orientation in guiding climate change risk perception. The main effect of the two factors was also investigated. A nationwide online survey (N = 592) was conducted in South Korea by a professional survey agent. When self-efficacy, trust, and other demographics were controlled for, multiple regression analyses revealed that those focusing on what is happening (diagnostic framing) rather than what-to-do (prognostic framing) had higher risk perception. More importantly, only conservatives showed significantly different levels of risk perception according to their framing of the issue. Conservatives inclined to diagnostic framing showed higher risk perception than conservatives favoring prognostic framing. This difference disappeared when it comes to South Korean liberals, indicating an interaction between individual framing and political orientation. The significance of investigating individual framing, not media framing, and their interaction with political orientation are discussed.     

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.     

A fuzzy logic-driven multiple knowledge integration framework for improving the performance of expert systems

To maintain a high performance in an ill-structured situation, expert systems should depend on multiple sources of knowledge rather than a single type. For this reason, we propose multiple knowledge integration by using a fuzzy logic-driven framework. Types of knowledge being considered here are threefold: machine, expert and user. Machine knowledge is obtained by a back- propagation neural network model from historical instances of a target problem domain. Expert knowledge is related to interpreting the trends of external factors that seem to affect the target problem domain. User knowledge represents a user’s personal views about information given by both expert knowledge and machine knowledge. The target problem domain of this paper is one-week-ahead stock market stage prediction: Bull, Edged-up, Edged-down, and Bear. Extensive experiments with real data proved that the proposed fuzzy logic-driven framework for multiple knowledge integration can contribute significantly to improving the performance of expert systems. Copyright © 1998 John Wiley & Sons, Ltd.     

基于模糊多属性方法的企业风险管理评价研究

企业风险管理是近些年逐渐发展起来的一门学科。随着风险管理引入企业管理活动,如何比较行业内不同企业的风险管理效果成为一个关键问题。本文在借鉴模糊多属性决策方法的基础上提出企业风险管理的评价模型,将区间数的判断矩阵转化为相离度矩阵,使用熵值对不同风险因素进行赋权,利用TOPSIS方法计算各企业的风险评价值,最终得出企业风险管理效果的判断标准,为衡量企业风险管理能力提供借鉴。     

Mortality,Health, and Marriage: A Study Based on Taiwan's Population Data

Life expectancy has been increasing significantly since the start of the 20th century, and mortality improvement trends are likely to continue in the 21st century. Stochastic mortality models are used frequently to predict the expansion in life expectancy. In addition to gender, age, period, and cohort are the three main risk factors considered in constructing mortality models. Other than these factors, it is also believed that marital status is related to health and longevity, and many studies have found that married persons have a lower mortality rate than the unmarried. In this study, we have used Taiwan's marital data for the whole population (married, unmarried, divorced/widowed) to evaluate if the marital status can be a preferred criteria. Furthermore, we also want to know whether the preferred criteria will be valid in the future. We chose two popular mortality models, the Lee-Carter and age-period-cohort, to model the mortality improvements for various marital statuses. Because of a linear dependence in the parameters of the age-period-cohort model, we used a computer simulation to choose the appropriate estimation method. Based on Taiwan's marital data, we found that married persons have significantly lower mortality rates than the single, and if converting the difference into a life insurance policy, the discount amount is even larger than that for smokers/nonsmokers.