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.     

A Model for Coronary Heart Disease and Stroke with Applications to Critical Illness Insurance Underwriting II: Applications

Abstract

In Part I we constructed a model for the development of coronary heart disease (CHD) or stroke that either incorporates, or includes pathways through, the major risk factors of interest when underwriting for critical illness (CI) insurance. In Part II we extend this model to include other critical illnesses, for example, cancers and kidney failure, and describe some applications of the model. In particular, we discuss CI premium ratings for applicants with combinations of some or all of high body mass index, smoking, high blood pressure, high cholesterol, and diabetes. We also consider the possible effect on CI premium ratings of genetic conditions that increase the likelihood of high blood pressure, high cholesterol, diabetes, CHD event, or stroke.     

Converting Clinical Literature to an Insured Population: A Comparison of Models Using Nhanes

Abstract

The use of clinical literature to set risk classification standards for life insurance underwriting stems from the need to set the most accurate standards using the best available information. A necessary hurdle in this process is converting any excess mortality observed in a clinical study to the appropriate rating for use in underwriting. A widely accepted model in the insurance industry, the Excess Death Rate model, treats the excess as additive to the conditional probability of death for an insurance company’s unimpaired class.

In this paper we test the validity of that model versus other common predictive models of excess mortality in an insured population. Applying these models to National Health and Nutrition Examination Survey (NHANES) data, we derive estimates for excess mortality from three commonly seen underwriting impairments in what could be considered a clinical population. These estimates are added to an estimate of an insurance company’s unimpaired mortality class and then used to predict deaths in an “insurable” subset of that clinical population.

The Excess Death Rate model performed the best of all models, having the smallest cumulative difference of actual to predicted deaths. The use of publicly available data, such as that in NHANES, could help bridge the gap between clinical literature and its application in insurance underwriting if insurable cohorts can be reliably identified from these generally healthy, ambulatory groups.     

The Brugada syndrome--an electrocardiogram with important mortality implications

The electrocardiogram (ECG) is a valuable screening tool for increased risk in underwriting life insurance applicants. This article discusses a recently described ECG pattern associated with a high risk of sudden unexpected death.     

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.     

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.     

Adult Polycystic Kidney Disease and Insurance

Abstract

Adult Polycystic Kidney Disease (APKD) is a single-gene autosomal dominant genetic disorder leading to end-stage renal disease (ESRD, meaning kidney failure). It is associated with mutations in either of two genes, APKD1 and APKD2, and although diagnosis is still mostly by ultrasonography rather than DNA-based tests, this may change in the future. Recent studies have shown that the rates of onset of ESRD associated with APKD1 mutations are much greater than those associated with APKD2 mutations, a form of genetic heterogeneity that differs from, for example, familial breast cancer. In this paper we model the the impact of mutations in APKD1 or APKD2 on critical illness insurance, extending the work of Gutiérrez and Macdonald (2003), which was based on studies predating DNA-based tests. We then extend the model to life insurance and show that the financial impact is strongly dependent on the availability of treatment (dialysis and transplant), but that if it is available, extra premiums for life insurance are modest. We show that genetic heterogeneity introduces a novel problem, because carrying an APKD2 mutation is less risky than having a family history of APKD. Thus, in jurisdictions where family history may be used in underwriting but genetic tests may not, it may be illegal to use knowledge that benefits the applicant.     

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.     

Contingent Commissions and the Management of the Independent Agency

Insurance agencies continue to exist as an important distribution mechanism because they give their contracting insurers advantages in risk selection and enable insurance applicants to transfer complex risks. While independent agencies are compensated by upfront commissions, a key component of their profitability is tied to contingent commissions. A contingency arrangement represents ex post compensation normally tied to underwriting profitability, volume, and annual growth. We report two actual contingency contracts in the context of a decision process for choosing among contingency offerings by insurers. We incorporate both uncertainty and correlation among key variables to arrive at values for competing contracts, then use a downside risk approach that helps agency owners select the better contract. The approach offered in this article is scalable to a selection problem for any number of contingency arrangements.     

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.     

Huntington's disease,critical illness insurance and life insurance

We describe briefly a model of Huntington's disease (HD), a highly penetrant, dominantly inherited, fatal neurological disorder. Although it is a single-gene disorder, mutations are variable in their effects, depending on the number of times that the CAG trinucleotide is repeated in a certain region of the HD gene. The model covers: (a) rates of onset, depending on CAG repeat length as well as age; (b) post-onset rates of mortality; and (c) the distribution of CAG repeat lengths in the population. Using these, we study the critical illness and life insurance markets. We calculate premiums based on genetic test results that disclose the CAG repeat length, or more simply on a family history of HD. These vary widely with age and policy term; some are exceptionally high, but in a large number of cases cover could be offered within normal underwriting limits. We then consider the possible costs of adverse selection, in terms of increased premiums, under various possible moratoria on the use of genetic information, including family history. These are uniformly very small, because of the rarity of HD, but do show that the costs would be much larger in relative terms if family history could not be used in underwriting. We point out some difficulties involved in applying a moratorium that recognises simply a dichotomy between ‘carriers’ and ‘non-carriers’ of any mutation in a gene when these mutations are, in fact, very variable in their effects. These complexities suggest that restrictions on the disclosure, rather than on the use, of genetic information, if it became established as a principle, could deprive insurers of information needed for risk management even if not used in underwriting.     

Relative Importance of Risk Sources in Insurance Systems

Abstract

Actuaries, and other managers of uncertainty, identify factors in modeling insurance risks because they believe (1) that these factors affect the outcome of a risk or (2) that the factors can be managed, thus allowing analysts a degree of control over the insurance system. This paper shows how to use a statistical measure, the coefficient of determination, for quantifying the relative importance of a source of uncertainty. With a quantitative measure of relative importance, risk managers can sharpen their intuition about the relative importance of risk factors and become better custodians of financial security systems.

This paper shows that the coefficient of determination is intuitively appealing in assessing the effectiveness of basic risk management techniques including risk exchange, pooling, and financial risk management. A single source common to all risks reduces the effectiveness of a pool; the risk measure quantifies the relative importance of this common source. The coefficient of determination is shown to have roots in the economics as well as the statistics literature. This connection provides further motivation for using the coefficient of determination and also suggests alternative measures for quantifying relative importance. The risk measure is useful in multivariate situations in which several factors affect a risk simultaneously. The paper illustrates this usefulness by considering a pool of policies that is subject to mortality, a common disaster, and a common investment environment.     

Underwriting lethal genetic diseases

There are thousands of single gene deposits that cause increased morbidity or mortality risks. Few have complete penetrance leading to certain death. Most can be underwritten with affordable increases in premium; many at standard rates. As we learn more about penetrance for specific mutations we can learn to be more aggressive in underwriting inherited risks. I have described approaches to underwriting untested applicants to Huntington disease, and tested applicants who carry dominant mutations leading to breast, ovarian and colon cancer.     

Mortality investigation among persons whose applications for insurance have heen rejected

Abstract

Extract

Life insurance companies are interested III investigations of the mortality among that group of applicants whose applications for insurance, for health reasons, have not been accepted. The compa. nies thereby obtain material enabling them to decide whether their rejection policy during a period has been too strict or not, and on which points, if any, the selection of risks can be liberalized.     

Improving risk classification and ratemaking using mixture-of-experts models with random effects

In the underwriting and pricing of nonlife insurance products, it is essential for the insurer to utilize both policyholder information and claim history to ensure profitability and proper risk management. In this paper, we apply a flexible regression model with random effects, called the Mixed Logit-weighted Reduced Mixture-of-Experts, which leverages both policyholder information and their claim history, to categorize policyholders into groups with similar risk profiles, and to determine a premium that accurately captures the unobserved risks. Estimates of model parameters and the posterior distribution of random effects can be obtained by a stochastic variational algorithm, which is numerically efficient and scalable to large insurance portfolios. Our proposed framework is shown to outperform the classical benchmark models (Logistic and Lognormal GL(M)M) in terms of goodness-of-fit to data, while offering intuitive and interpretable characterization of policyholders' risk profiles to adequately reflect their claim history.     

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.     

Relationship Banking and the Pricing of Financial Services

We investigate pricing effects of the joint production of loans and security underwritings. We control for firm and borrower characteristics, including differences in sequencing, which are important for pricing. Contrary to previous studies, when banks combine lending and underwriting within the same customer relationship they charge premiums for both loans and underwriting services. Abstracting from effects of joint production within relationships, depository banks engaged in underwriting price lending and underwriting more cheaply than stand alone investment banks. One advantage borrowers enjoy from bundling products within a banking relationship is a form of liquidity risk insurance, which is manifested in a reduced demand for lines of credit. We also find evidence of a “road show” effect; firms enjoy loan pricing discounts on loans that are negotiated at times close to the debt underwritings, whether or not the same bank provides both services. Relationship effects are only visible when lending and underwriting both occur, and are stronger for equity-loan relationships than for debt-loan relationships. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

Underwriting profit margin of P/L insurance in the fuzzy-ICAPM

The ICAPM is used to study the underwriting profit margin of the P/L insurance company, including the insurances of automobile damage, automobile liability and fire, in which the parameters are the symmetric or non-symmetric triangular fuzzy numbers. From the ten-year data of a company in Taiwan we determine the lower and upper limits associated with the various α-level of the fuzzy numbers. Our results show that the best-fitting parameters of the model from our data are the asymmetric triangular fuzzy numbers. The skew factors in each insurance are determined, which could be used to perform the forecasting of the underwriting profit margin. Our results show that the systematic risk in the fuzzy environment (with best-fitting value of skew factor) becomes larger than that in the crisp environment. However, the insurance underwriting leverage and insurance financial leverage in the fuzzy environment are smaller than those in the crisp environment. JEL Classification G22 · G32 The author is grateful to the two anonymous reviewers for The Geneva Risk and Insurance Review for their comments on an earlier version of this paper.     

Underwriting and investment risks in the property-liability insurance industry: evidence prior to the 9–11 event

Underwriting and investment are two important and related business activities of insurance companies. However, studies on the interrelation between underwriting and investment risks of Property-Liability (P-L) insurance companies are sparse in the literature. Using a sample of US P-L insurers, this article conducts an empirical investigation of how these two risks are associated with each other in the 1994–2000 period (before the September 11th terrorist attack in 2001). Our results, robust to various estimations, suggest that there is no significant relationship between the underwriting and investment risks among our sample firms. Such results based on pre 9–11 event period provide some support for the conjecture of Achleitner et al. (Geneva Pap Risk Insur Issues Pract 27:275–282, 2002) that many insurance companies may have failed to take an integrated approach to risk management. This resulted in a heavy loss due to dual exposures in both underwriting and investment in the 9–11 event. In the aftermath of the recent global financial crisis, risk taking and risk management of financial institutions have received more attention and increasing scrutiny. We believe the current paper provides some useful insights in this vein.     

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.