Effective Underwriting in the Genetic Testing Era

This paper notes that prior to the availability of genetic test results, conventional life insurance underwriting had produced satisfactory mortality results even though a number of applicants insured at standard or better must have had serious genetic markers. The paper discusses the problems that may affect underwriting when an applicant is aware of a genetic risk factor.

The paper suggests use of pre-genetic testing era underwriting methodology, including medical history and family history, with strict financial underwriting to control antiselection. A set of underwriting rules is provided. The need for a sales organization that can produce a substantial amount of business is cited as necessary for success.

To spread equitably any excess cost on account of insuring persons with genetic markers, a risk pool is suggested. The pool manager would also inform a company of additional applications to other companies by genetically impaired applicants.

The purpose of the proposal is to deflect ill-advised political solutions and, at the same time, to control expenses by ensuring a high ratio of paid-for policies to applications.     

Questionnaire based mortality assessment: an exploratory analysis of NHANES III

The need for speed and efficiency in life insurance underwriting has never been greater. With increasing acquisition costs, the need for timeliness to complete the sales process, and the need for accurate mortality prediction a great deal of resources have been devoted to the development of non-traditional underwriting processes and criteria in hopes of streamlining the process. In this paper, we describe an exploratory analysis of mortality linked data from the US NHANES III study. Our goal for this analysis was to identify mortality predictors that would be good candidates for further investigation in insurance applicants, especially in the context of simplified issue products which focus on younger age applicants. We identified aerobic exercise, dental health, alcohol beverage type and quantity, and dietary components and patterns as factors that may hold promise as mortality predictors in persons age 17-65. Though the limitations of this analysis preclude the immediate use of these factors as underwriting criteria, it does appear that several of these hold promise, and should be tested in an insurance application context. Focus groups, market testing, or even insertion as non-actionable questions in a subset of applications may be ways to collect further data on them.     

Pricing Term Insurance in the Presence of a Family History of Breast or Ovarian Cancer

Abstract

We estimate the increased mortality and term life insurance costs for women who have a family history of breast or ovarian cancer. Using data from the medical literature on age-specific and family history-specific incidence rates, we develop double-decrement models to evaluate the actuarial impact of breast cancer and ovarian cancer in the family. We also calculate the increased mortality and term insurance costs for women who test positive for the BRCA1 or BRCA2 gene mutation. We find that the type of affected relative and her age at onset of the disease are key underwriting factors. We find substantial mortality increases (up to 100%) for women with two relatives with cancer and women with a first-degree relative who developed cancer at an early age. Mortality increases for women with the BRCA gene mutation reach 150%. While some females with a family history of cancer can be accepted at standard rates, others may need to be quoted substandard rates, depending on the underwriting policy of the company. Females with the gene mutation can possibly be accepted at a rate that incorporates a severe mortality surcharge.     

Peripartum cardiomyopathy: mortality outcomes

Mortality estimates of peripartum cardiomyopathy have been reported to be between 18 and 56% without reference to time frames. Although this is an unusual impairment, medical directors need accurate information to meet the gold standard of underwriting: decisions must be based on sound underwriting and actuarial principles reasonably related to actual or anticipated loss experience. In an insurance purchasing population, the excess mortality in peripartum cardiomyopathy can be nearly eliminated by not insuring those with the impairment within the first 6 months postpartum or until all abnormal physiologic parameters have resolved. Thereafter, the risk is probably negligible. This abstract illustrates the challenge to determine expected mortality when the study population exhibits strong racial diversity and when available expected life tables contain raw data of only alive and dead at each yearly interval.     

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.     

Seasonal mortality for fractional ages in short term life insurance

Abstract

Fernández-Durán, and Gregorio-Domínguez, Seasonal Mortality for Fractional Ages in Life Insurance. Scandinavian Actuarial Journal. A uniform distribution of deaths between integral ages is a widely used assumption for estimating future-lifetimes; however, this assumption does not necessarily reflect the true distribution of deaths throughout the year. We propose the use of a seasonal mortality assumption for estimating the distribution of future-lifetimes between integral ages: this assumption accounts for the number of deaths that occurs in given months of the year, including the excess mortality that is observed in winter months. The impact of this seasonal mortality assumption on short-term life insurance premium calculations is then examined by applying the proposed assumption to Mexican mortality data.     

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.     

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.     

A new parametric model for converting excess mortality from clinical studies to insured population

We propose a new parametric model – the generalized excess mortality (GEM) model – for converting excess mortality from clinical to insured population. The GEM model has been formulated as a generalization of the excess death rate (EDR) model in terms of a single adjustment parameter (m) that accounts for a partial elimination of a clinical study’s EDR due to the underwriting selection process. The suggested value of the parameter m depends only on the ratio of the impairment’s prevalence rate in the insured population to that in the clinical population. The model’s development has been implemented in two phases: the design phase and the validation phase. In the design phase, the data from the National Health and Nutrition Examination Survey I pertaining to three broad impairments (diabetes, coronary artery disease, and asthma) have been used. As a result, the following equation for the parameter m has been proposed: m_k?=?(P_i,k/P_c,k)ⁿ, where P_i,k, P_c,k are the prevalence rates of impairment k under study in the insured and the clinical populations, respectively, and n a single universal parameter with its value best approximated as n?=?0.5 (95% confidence interval 0.5–0.6). In the validation phase, several independent clinical studies of three other impairments (Crohn’s disease, epilepsy, and chronic obstructive pulmonary disease) were used. As it has been demonstrated in the validation phase, for a number of impairments, the GEM model can provide a better fit for observed insured population mortality than either one of the conventional EDR or mortality ratio models.     

Structured settlement annuities, part 1: overview and the underwriting process

Structured settlement underwriting is the underwriting of medically impaired lives for the purchase of an annuity to fund the settlement. Other than risk assessment, structured settlement (SS) underwriting has little in common with traditional life insurance underwriting. Most noteworthy of these differences is the relative lack of actuarial data on which to base decisions about mortality and the necessity for prospective thinking about risk assessment. The purpose of this paper is to provide a foundation for understanding the structured settlement business and to contrast the underwriting of structured settlements with that of traditional life insurance. This is the first part of a two-part article on SS annuities. Part 2 deals with the mortality experience in SS annuitants and the life-table methodology used to calculate life expectancy for annuitants at increased mortality risk.     

Genetics,Alzheimer’s Disease,and Long-Term Care Insurance

Abstract

This paper applies a model of Alzheimer’s disease (AD) developed by Macdonald and Pritchard (2000) to the question of the potential for adverse selection in long-term care (LTC) insurance introduced by the existence of DNA tests for variants of the ApoE gene, the ε4 allele of which is known to predispose one to earlier onset of AD. It computes the expected present values (EPVs) of model LTC benefits with respect to AD for each of five ApoE genotypes, weighted average EPVs with and without adverse selection, and sample underwriting ratings. The paper concludes that adverse selection could increase costs significantly in a small LTC insurance market only if current population genetic risk is not much smaller than that observed in case-based studies, and if carriers of the ε4 allele are very much more likely to buy LTC insurance. Finally, the paper considers the cost of a combined retirement package, providing both pension and LTC insurance, and shows that it can reduce adverse selection.     

Comparison of body mass index and waist circumference as predictors of all-cause mortality in a male insured lives population

Obesity assessed by body mass index (BMI) is associated with increased mortality risk, but there is uncertainty about whether BMI is the best way to measure obesity. Waist circumference (WC) has been proposed as a better measure. The Swiss Re BMI/WC Study was conducted to determine whether BMI or WC is a better predictor of future all-cause mortality in a large male insurance population. Using Cox proportional hazard models, risk ratios for increasing BMI and WC were 1.033 (P < .001) and 1.027 (P < .001), respectively. Risk ratios for obesity defined by BMI > or = 30 kg/m2 and WC > or = 40 inches were 1.33 (P < .001) and 1.20 (P = .002), respectively. In this study, BMI and WC are essentially equivalent in their ability to predict mortality risk in a male insurance population. Obesity, measured by either BMI or WC, has important underwriting and pricing implications.     

Geologisches Risikomanagement für Versicherungen

The application of Geoinformationsystems under geological, hydrological and hydrogeological aspects for the risk management is a further development of the geographical underwriting of the insurance industry. The knowledge of the geology, hydrology and hydrogeology is fundamental for the understanding and spatial analysis of insured objects before and during loss events for example with contaminations of the aquifer. Furthermore possible loss scenarios could be prevented or minimized if the subsurface geology and hydrogeology are already known and integrated in the initial insurance appraisal. The modelling and classification of the geoscientific knowledge also enables the definition of Action Zones, which allow a better appraisal and assessment of the insurable objects. This leads to an optimized and transparent premium calculation for both, the insurance and the policyholder (Münchener Rück 2002). The visualization of the geoscientific subsurface information in Geoinformationsystems is simple and economical feasible, it is quick to analyze and combinable with additional information and gives important insights in the subsurface structures. The paper describes a workflow how such Action Zones could be assessed and the additional information for the premium is generated.     

Mortality risk assessment in the elderly: the utility of delayed word recall

Cognitive impairment is an important predictor of mortality in the elderly. An extended delayed word recall (DWR) is one of the most sensitive tests for cognitive impairment. A mortality study was performed on a population of long-term care insurance applicants aged 70 and older who were underwritten during the years 1995-2003 and who had cognitive testing by DWR. Within this relatively short period of time, individuals with DWR score of 0-5 compared to those with DWR score of 6-10 had a markedly worse mortality outcome overall and also when analyzed by gender, underwriting age, underwriting year or smoking status.     

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.     

The Theory of Optimal Stochastic Control as Applied to Insurance Underwriting Cycles

We use the theories of optimal stochastic control and engineering process control to analyze the well-known phenomenon of insurance underwriting cycles in continuous time. We show in a continuous time framework that underwriting cycles can be explained with a model where premiums are set rationally, but where there are various reporting and regulatory lags. We find that the observed cycle length depends on the length of these underlying lags. Our result can be seen as consistent with previous empirical work showing underwriting cycles varying across countries and lines of insurance. In the event that no lags exist, our result is also consistent with more recent literature suggesting that insurance cycles may not exist.     

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.     

Compound Poisson Model with Covariates

Abstract

Pet insurance in North America continues to be a growing industry. Unlike in Europe, where some countries have as much as 50% of the pet population insured, very few pets in North America are insured. Pricing practices in the past have relied on market share objectives more so than on actual experience. Pricing still continues to be performed on this basis with little consideration for actuarial principles and techniques. Developments of mortality and morbidity models to be used in the pricing model and new product development are essential for pet insurance. This paper examines insurance claims as experienced in the Canadian market. The time-to-event data are investigated using the Cox’s proportional hazards model. The claim number follows a nonhomogenous Poisson process with covariates. The claim size random variable is assumed to follow a lognormal distribution. These two models work well for aggregate claims with covariates. The first three central moments of the aggregate claims for one insured animal, as well as for a block of insured animals, are derived. We illustrate the models using data collected over an eight-year period.     

保险公司资产组合与最优投资比例研究

保险公司收益主要来源于承保利润和投资收益,其中承保利润受政策变动、市场条件等外部环境的影响较大,而投资收益则更多地取决于保险公司的投资能力,因此保险公司如何构建资产组合、如何确定最优投资比例就是获取投资收益最大化的重要因素。本文通过理论推导得出了保险公司的资产组合模型并运用非线性规划求解出最优投资比例,进而根据保险公司的投资数据进行了实证研究,为我国保险公司的资产组合及最优投资比例提供了一个可借鉴的思路。     

Markovian Approaches to Joint-Life Mortality

Abstract

Many insurance products provide benefits that are contingent on the combined survival status of two lives. To value such benefits accurately, we require a statistical model for the impact of the survivorship of one life on another. In this paper we first set up two models, one Markov and one semi-Markov, to model the dependence between the lifetimes of a husband and wife. From the models we can measure the extent of three types of dependence: (1) the instantaneous dependence due to a catastrophic event that affect both lives, (2) the short-term impact of spousal death, and (3) the long-term association between lifetimes. Then we apply the models to a set of jointlife and last-survivor annuity data from a large Canadian insurance company. Given the fitted models, we study the impact of dependence on annuity values and examine the potential inaccuracy in pricing if we assume lifetimes are independent. Finally, we compare our Markovian models with two copula models considered in previous research on modeling joint-life mortality.