Anorexia nervosa: a 63-year population-based survival study

As eating disorders attract increasing publicity, more affected individuals will seek medical attention. Many will have needs for life insurance. Due to selection bias, most of the literature on anorexia nervosa (AN) presents an unfavorable prognosis. Therefore, the impairment is considered an adverse life insurance risk. This review is from an unselected, community population. The demographics of the study population and its expected mortality are similar to a population purchasing life insurance products. Comparative experience over 63 years of follow-up reveals mortality ratios and excess death rates similar to those expected for the population. High-risk comorbid diagnoses of depression and alcoholism are discussed.     

A Bayesian non-parametric model for small population mortality

This paper proposes a Bayesian non-parametric mortality model for a small population, when a benchmark mortality table is also available and serves as part of the prior information. In particular, we extend the Poisson-gamma model of Hardy and Panjer to incorporate correlated and age-specific mortality coefficients. These coefficients, which measure the difference in mortality levels between the small and the benchmark population, follow an age-indexed autoregressive gamma process, and can be stochastically extrapolated to ages where the small population has no historical exposure. Our model substantially improves the computation efficiency of existing two-population Bayesian mortality models by allowing for closed form posterior mean and variance of the future number of deaths, and an efficient sampling algorithm for the entire posterior distribution. We illustrate the proposed model with a life insurance portfolio from a French insurance company.     

Redistribution and Insurance: Mandatory Annuitization With Mortality Heterogeneity

This article examines the distributional implications of mandatory longevity insurance when mortality heterogeneity exists in the population. Previous research has demonstrated the significant financial redistribution that occurs under alternative annuity programs in the presence of differential mortality across groups. This article embeds that analysis into a life‐cycle framework that allows for an examination of distributional effects on a utility‐adjusted basis. It finds that the degree of redistribution that occurs from the introduction of a mandatory annuity program is substantially lower on a utility‐adjusted basis than when evaluated on a purely financial basis. In a simple life‐cycle model with no bequests, complete annuitization is welfare enhancing even for those with higher‐than‐average expected mortality rates, so long as administrative costs are sufficiently low. These findings have implications for policy toward annuitization, particularly as part of a reformed Social Security system.     

Mortality Inequality in Finland*

We study inequality in mortality in Finland using registry data that cover the whole population for years 1990–2018. We create municipality‐level indices of regional deprivation (poverty rate), and show how age‐specific mortality rates have evolved across regions and over time. The inequality in mortality has been remarkably low over the time period for most age groups. However, among young and prime‐age males, the mortality rates have been persistently higher in the poorer areas. For these age groups, the leading causes of death are deaths of despair (alcohol and suicides) and accidents. For the cohorts that were young during the deep recession of the early 1990s, we also document higher inequality in middle‐age mortality than for cohorts entering the labour market in recovery periods.     

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.     

Application of Relational Models in Mortality Immunization

The prediction of future mortality rates by any existing mortality models is hardly exact, which causes an exposure to mortality (longevity) risk for life insurers (annuity providers). Since a change in mortality rates has opposite impacts on the surpluses of life insurance and annuity, hedging strategies of mortality and longevity risks can be implemented by creating an insurance portfolio of both life insurance and annuity products. In this article, we apply relational models to capture the mortality movements by assuming that the realized mortality sequence is a proportional change and/or a constant shift of the expected one, and the size of the changes varies in the length of the sequences. Then we create a variety of non-size-free matching strategies to determine the weights of life insurance and annuity products in an insurance portfolio for mortality immunization, where the weights depend on the sizes of the proportional and/or constant changes. Comparing the hedging performances of four non-size-free matching strategies with corresponding size-free ones proposed by Lin and Tsai, we demonstrate with simulation illustrations that the non-size-free matching strategies can hedge against mortality and longevity risks more effectively than the size-free ones.     

Die demographische Entwicklung in Deutschland und ihre Bedeutung für das Kapitaldeckungsverfahren von Lebensversicherern,privaten Krankenversicherern und Pensionsfonds

The decline in population will increase dramatically after the year 2030; this development is accompanied by a dramatic change of the social structure of the German society and the aging of the population. Policyholders of annuity contracts who are now in the age of 35 will probably retire in the year 2037 and their death can be actuarially awaited near 2060. That means those people are completely affected by the development after 2030. The annuity contracts with a guaranteed interest rate (legally fixed for the duration of the contracts) dominate the new business of life insurance companies. The period of time of the interest rate guarantee can be up to 40 or 50 years. Our demographic profile leads to the assumption that in 2050 we will miss 15 million people of our working population; this represents the actual figure of the working population of Belgium, Denmark, Finland, Ireland and Austria. Consumption, overall investments and the demand of borrowed funds will decrease. The level of the rate of return of bonds or other interest bearing assets will decline. On the other hand, the value of shares of those companies who belong to the winners of the global transition process we have started right now will increase. Unfortunately life insurance companies and pension funds — when they take investment risk — are forced mainly to invest in bonds or other debentures. The consequence can be a not attractive level of return of the premiums paid. A solution would be to reinforce the development and business of non guaranteed annuities and a higher quote of shares in the portfolios. Then it would be the duty of each policyholder to protect himself by diversification     

Continuous-time multi-cohort mortality modelling with affine processes

Continuous-time mortality models, based on affine processes, provide many advantages over discrete-time models, especially for financial applications, where such processes are commonly used for interest rate and credit risks. This paper presents a multi-cohort mortality model for age-cohort mortality rates with common factors across cohorts as well as cohort-specific factors. The mortality model is based on well-developed and used techniques from interest rate theory and has many applications including the valuation of longevity-linked products. The model has many appealing features. It is a multi-cohort model that describes the whole mortality surface, it captures cohort effects, it allows for observed imperfect correlation between different cohorts, it is shown to fit historical data at pension-related ages very well, it has closed-form expressions for survival curves and we show that it outperforms a number of other commonly used discrete-time mortality models in forecasting future survival curves.     

A partial internal model for longevity risk

This paper proposes a simple partial internal model for longevity risk within the Solvency 2 framework. The model is closely linked to the mechanisms associated with the so-called Danish longevity benchmark, where the underlying mortality intensity and the trend is estimated yearly based on mortality experience from the Danish life and pension insurance sector, and on current data from the entire Danish population. Within this model, we derive an estimate for the 99.5% percentile for longevity risk, which differs from the longevity stress of 20% from the standard model. The new stress explicitly reflects the risk associated with unexpected changes in the underlying population mortality intensity on a one-year horizon and with a 99.5% confidence level. In addition, the model contains a component, which quantifies the unsystematic longevity risk associated with a given insurance portfolio. This last component depends on the size of the specific portfolio.     

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.     

Product innovation and population dynamics in the German insurance market

Empirical research in organizational ecology has mainly focused on analyzing founding and mortality rates using life history data of the organizations. We try to extend this approach in our study in a number of ways. In contrast to most empirical studies in organizational ecology, we chose a population of service organizations, in particular the German insurance companies, the development dynamics of which are rather obvious in the innovative activities of existing organizations than in founding activities. We further discuss the points of contact between the organizational ecology approach and the theory of industry life cycles and extend the analysis to the relationship between innovative activities and population dynamics. The study examines the effects of population density, former events, and organizational size and age structure in the population of property &; casualty insurance companies on the number of product innovations generated. We will further develop a concept for an insurance specific industry life cycle with a non-typical maturation and degeneration phase.     

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.     

Lifetime asset allocation with idiosyncratic and systematic mortality risks

This paper considers a lifetime asset allocation problem with both idiosyncratic and systematic mortality risks. The novelty of the paper is to integrate stochastic mortality, stochastic interest rate and stochastic income into a unified framework. An investor, who is a wage earner receiving a stochastic income, can invest in a financial market, consume part of his wealth and purchase life insurance or annuity so as to maximize the expected utility from consumption, terminal wealth and bequest. The problem is solved via the dynamic programming principle and the Hamilton–Jacobi–Bellman equation. Analytical solutions to the problem are derived, and numerical examples are provided to illustrate our results. It is shown that idiosyncratic mortality risk has significant impacts on the investor’s investment, consumption, life insurance/annuity purchase and bequest decisions regardless of the length of the decision-making horizon. The systematic mortality risk is largely alleviated by trading the longevity bond. However, its impacts on consumption, purchase of life insurance/annuity and bequest as well as the value function are still pronounced, when the decision-making horizon is sufficiently long.     

Regression-based algorithms for life insurance contracts with surrender guarantees

We present a general framework for pricing life insurance contracts embedding a surrender option. The model allows for several sources of risk, such as uncertainty in mortality, interest rates and other financial factors. We describe and compare two numerical schemes based on the Least Squares Monte Carlo method, emphasizing underlying modeling assumptions and computational issues.     

Forecasting mortality

Abstract

The work of actuaries is concerned with estimating the future on the basis of past experience. The calculation of a premium to be charged for a given risk implies a forecast of the future but so far as mortality is concerned we have generally been content to examine past experience and assume that the results will be repeated. Judged as forecasts our estimates have sometimes been wide of the mark and owing to an almost continuous improvement in mortality actuaries have been assuming heavier rates of mortality than have been experienced. We may defend the use of past experience by saying that it is on the safe side when we are calculating premiums and we may argue that it is the best practical method; but an alternative is to make a more accurate forecast and then allow in our calculations a margin for chance deviations, emergencies, etc. Moreover the assumption that the past will be repeated has not been uniformly safe; it has led to bad results in annuity business and may prove unfortunate in social insurance, pension funds, and even sickness insurance. For some of these purposes we should either work on an estimate of future rates of mortality or, which comes to much the same thing, take a sufficient margin to cover the error involved in our assumptions.     

Der neue Standard zur bilanziellen Abbildung von Versicherungsverträgen (IFRS 17) – Eine kritische Analyse der Auswirkungen auf die Versicherungsbranche

The new standard for the accounting of insurance contracts (IFRS 17) will entail substantial changes for the insurance industry. In the following article the new standard is critically analyzed. First and foremost the coming valuation model, the so-called building block approach, is presented which will be the basis for all insurance contracts within the scope of IFRS 17. (For certain insurance contracts, especially those with direct participation features, or for less complex or short-term insurance contracts, there are some modifications.) To be more precise, IFRS 17 introduces an enterprise-specific valuation approach that is grounded on the so-called fulfilment value. This fulfilment value is determined by four separate building blocks (fulfilment-cashflow, discount rate, risk margin and contractual service margin), which will be addressed in detail. Finally, major changes in performed accounting practices that insurance enterprises are confronted with and will have to adapt to in their financial statements and accounts are pointed out.     

On systematic mortality risk and risk-minimization with survivor swaps

A new market for so-called mortality derivatives is now appearing with survivor swaps (also called mortality swaps), longevity bonds and other specialized solutions. The development of these new financial instruments is triggered by the increased focus on the systematic mortality risk inherent in life insurance contracts, and their main focus is thus to allow the life insurance companies to hedge their systematic mortality risk. At the same time, this new class of financial contract is interesting from an investor's point of view, since it increases the possibility for an investor to diversify the investment portfolio. The systematic mortality risk stems from the uncertainty related to the future development of the mortality intensities. Mathematically, this uncertainty is described by modeling the underlying mortality intensities via stochastic processes. We consider two different portfolios of insured lives, where the underlying mortality intensities are correlated, and study the combined financial and mortality risk inherent in a portfolio of general life insurance contracts. In order to hedge this risk, we allow for investments in survivor swaps and derive risk-minimizing strategies in markets where such contracts are available. The strategies are evaluated numerically.     

Use of a Markov Model to Estimate Long-Term Insured Lives’ Mortality Risk Associated With BRCA1 and BRCA2 Gene Mutations

Abstract

There is uncertainty regarding the degree of insurance risk associated with BRCA1/2, the gene mutations associated with breast cancer. Most reports to date have been based on high-risk populations selected from families with multiple and/or early-onset cancers; more favorable data have been reported in studies without this selection bias.

This paper discusses use of a Markov model to estimate mortality risk associated with BRCA1/2 gene mutations in female life insurance applicants. The goal is to derive a range of risk estimates based on different assumptions of breast and ovarian cancer incidence. A particular strength of the model is that transition probabilities after cancer diagnosis vary with age and cancer stage, as do excess hazard rates.

Data calculated by the model indicate that no single mortality curve characterizes risk for all life insurance applicants with a BRCA1/2 mutation. Rather, mortality risk depends on breast and ovarian cancer incidence rates and subsequent mortality rates, and on the method used to deal with competing breast and ovarian cancer incidence and mortality rates. Further refinement of risk estimates will depend on better incidence data and on resolution of complex statistical problems, such as informative censoring.

Widespread use of genetic information by insurance consumers could have important economic implications. For companies that sell individually underwritten products, profitability might decrease. Consumers might find higher prices and reduced availability, with a corresponding decrease in quantity of insurance purchased. Insurance and consumer ramifications would vary by cover, with living-benefit products, such as critical-illness insurance, most adversely affected. Societal choices are limited. Given assumptions in the cited scenario, it is likely premiums would rise and quantity of insurance purchased would decrease even with no change in existing social policy; attempted legal or regulatory remedies would further accentuate price increases and reductions in quantity purchased.     

Longevity and adjustment in pension annuities,with application to Finland

The aim of this paper is twofold. First, the improvement in adult mortality in Finland is studied. Lee-Carter (LC) Poisson log-bilinear model is used for mortality forecasting. Secondly, the paper studies how the pension annuities are adjusted to unexpected mortality pattern. A formula for funded plan is proposed. Application is made with Finnish mortality rates predicted using the LC model.