Medical savings accounts: why do they work?

This article analyzes and reviews the cost and design characteristics of medical savings accounts (MSAs). By placing premium savings from high-deductible health insurance in medical savings accounts, individuals have an incentive to shop for medical services. A more market-oriented health insurance and delivery system results, as individuals are now both users and buyers of health care. Data show that most families would accumulate balances in their MSAs that may be used for future medical expenses or savings. Through program design, the potential problems of adverse selection and cost to risk can be greatly reduced.     

Public Versus Private Insurance with Dual Theory: A Political Economy Argument

This paper analyzes the political support for public insurance in the presence of a private insurance alternative. The public insurance is compulsory and offers a uniform insurance policy. The private insurance is voluntary and can offer different insurance policies. Adopting Yaari's [Econometrica, 55, 95–115, 1987] dual theory to expected utility (i.e., risk aversion without diminishing marginal utility of income), we show that adverse selection on the private insurance market may lead a majority of individuals to prefer public insurance over private insurance, even if the median risk is below the average risk (so that the median actually subsidizes high-risk individuals). We also show that risk aversion makes public insurance more attractive and that the dual theory is less favourable to a mixed insurance system than the expected utility framework. Lastly, we demonstrate how the use of genetic tests may threaten the political viability of public insurance.     

Understanding the Shift in Demand for Cash Value Life Insurance

Ownership of cash value life insurance in the United States has fallen in recent decades. Changes in age cohorts, family composition, and tax laws may have contributed to this decline. We identify factors that influence the demand for cash value life insurance and test whether they alone can explain the sharp decline in ownership. Demographic and tax code changes do not explain the decrease in permanent insurance. There is a consistent downward trend in demand from 1992 to 2010—particularly among middle‐age and younger households. The fewer households who own cash value policies are on average wealthier and more financially sophisticated, suggesting that permanent life insurance is increasingly being used as a tax shield rather than as a hedge against a loss in human capital.     

Optimal health insurance

I formulate expected-utility-maximizing models for health insurance with a single optimal coinsurance (C*) and (separately) a single optimal deductible (D*). While so-doing, I formalize Nyman's challenge to standard welfare-loss models, clarifying when and by how much this alters unadjusted models. Using MEPS-calibrated lognormal distributions and incorporating skewness and kurtosis measures of financial risk, I show how C* shifts as various economic parameters change. For reasonable parameter values, C* < 0.1, much lower than variance-only estimates would conclude. Omitting higher-order risk parameters importantly understates risk and hence understates optimal insurance coverage. I separately develop methods to determine D*, showing that it is approximately a fixed percentage of income that falls as the distribution of financial risks rise. This finding contrasts with existing US public policy regarding high-deductible health plans, which employ fixed deductibles, independent of income.     

Stochastic Analysis of the Interaction Between Investment and Insurance Risks

Abstract

A portfolio of different insurance policies, such as temporary, endowment, and whole life, is studied in a stochastic mortality and interest environment. The first two moments of the present value of the benefits of the portfolio are derived. The riskiness of the portfolio as measured by the variance of the present value of the benefits can be divided into an insurance risk and an investment risk in two different ways. One way leads to a more natural interpretation of the two risk components. A simple portfolio is used to illustrate the results.     

Marktversagen auf dem geförderten Pflegezusatzversicherungsmarkt?

This study analyzes the supply side of the private German long term care insurance market. It compares loads and comprehensiveness of subsidized and unsubsidized insurance policies for three age groups. The results show that subsidized insurance policies are less comprehensive than unsubsidized insurance policies. In addition the premiums of subsidized policies are marked up substantially above expected benefits compared to unsubsidized policies. All in all these results indicate market failure due to adverse selection within the subsidized private long term care insurance market. Furthermore, the results show that due to unisex pricing, private long term care policies are in general more attractive to women than to men. As this is not reflected in demand, other factors than supply side failure seem to contribute to an overall low demand for private long term care insurance policies.     

Mortality-Indexed Annuities Managing Longevity Risk Via Product Design

Abstract

Longevity risk has become a major challenge for governments, individuals, and annuity providers in most countries. In its aggregate form, the systematic risk of changes to general mortality patterns, it has the potential for causing large cumulative losses for insurers. Since obvious risk management tools, such as (re)insurance or hedging, are less suited for managing an annuity provider’s exposure to this risk, we propose a type of life annuity with benefits contingent on actual mortality experience.

Similar adaptations to conventional product design exist with investment-linked annuities, and a role model for long-term contracts contingent on actual cost experience can be found in German private health insurance. By effectively sharing systematic longevity risk with policyholders, insurers may avoid cumulative losses.

Policyholders also gain in comparison with a comparable conventional annuity product: Using a Monte Carlo simulation, we identify a significant upside potential for policyholders while downside risk is limited.     

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.     

Adverse Selection in Term Life Insurance Purchasing due to the BRCA1/2 Genetic Test and Elastic Demand

Consumer groups fear that the use of genetic testing information in insurance underwriting might lead to the creation of an underclass of individuals who cannot obtain insurance; thus, these groups want to ban insurance companies from accessing genetic test results. Insurers contend that such a ban might lead to adverse selection that could threaten their financial solvency. To investigate the potential effect of adverse selection in a term life insurance market, a discrete‐time, discrete‐state, Markov chain is used to track the evolution of twelve closed cohorts of women, differentiated by family history of breast and ovarian cancer and age at issue of a 20‐year annually renewable term life insurance policy. The insurance demand behavior of these women is tracked, incorporating elastic demand for insurance. During the 20‐year period, women may get tested for BRCA1/2 mutations. Each year, the insurer calculates the expected premiums and expected future benefit payouts which determine the following year's premium schedule. At the end of each policy year, women can change their life insurance benefit, influenced by their testing status and premium changes. Adverse selection could result from (i) differentiated benefits following test results; (ii) differentiated lapse rates according to test results; and (iii) differentiated reactions to price increases. It is concluded that with realistic estimates of behavioral parameters, adverse selection could be a manageable problem for insurers.     

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.     

A decision theoretic formulation of insurance risk theory

Abstract

In a number of papers Borch has shown how certain insurance problems can be formulated using the concept of utility. (See Borch [3], [4], [5], [6], [7] and [8].) Borch's work is used as a building block in Part I of this report, which presents a Bayesian decision theoretic formulation of some of the main aspects of insurance risk theory. Part I makes use of the concepts of utility and subjective probability. It is admitted that these concepts are more commonly associated with individuals rather than groups of individuals such as insurance companies. However, in this report, we will refer to an insurance company as an individual (albeit a neuter one) and assume that it can quantify its preferences for consequences and its opinions about the occurrence of events. Further, we assume that a company “behaves” according to certain rules of consistent behavior which imply that when presented with several risky courses of action, the company will take the action which has the greatest expected utility. Formal treatments of assumptions that lead to this mode of behavior can be found in Savage [17] and Pratt, Raiffa, and Schlaifer [15].     

Out-of-Pocket Health Expenditures: A Suggested Role for Social Security

We present economic data to demonstrate that the (random) out-of-pocket health-related expenses of seniors who face medical problems are significant and increasing over time. This remains the case even when we take into account the availability of supplemental health insurance. We propose to apply a modest part of Social Security benefits, without increasing the total expenses of this system, to provide mandatory supplemental health insurance for all recipients. Using a theoretical framework we demonstrate that introducing such additional role for Social Security makes individuals (ex ante) better off and hence results in a Pareto dominating new regime for Social Security.     

Subsidization and Choice in the Group Health Insurance Market

This study investigates the effect of group health insurance plan choice on insurance unit price. The empirical findings suggest that the unit price of insurance, as measured by the ratio of the premium to expected indemnity benefits, is lower in group plans that offer employees a choice of different insurance options and require a premium contribution than it is in plans lacking at least one of these two features. The analyses suggest that lower unit prices are related to an increase in indemnity benefits and that the reduction in the unit price is greater for lower risks. The findings indicate that although subsidization of high risks by low risks occurs with group health insurance, the degree of subsidization is less when employees are offered a choice of health insurance plans.     

Cybersecurity insurance and risk-sharing

In today’s interconnected digital world, cybersecurity risks and resulting breaches are a fundamental concern to organizations and public policy setters. Accounting firms, as well as other firms providing risk advisory services, are concerned about their clients’ potential and actual breaches. Organizations cannot, however, eliminate all cybersecurity risks so as to achieve 100% security. Furthermore, at some point additional cybersecurity measures become more costly than the benefits from the incremental security. Thus, those responsible for preventing cybersecurity breaches within their organizations, as well as those providing risk advisory services to those organizations, need to think in terms of the cost-benefit aspects of cybersecurity investments. Besides investing in activities that prevent or mitigate the negative effects of cybersecurity breaches, organizations can invest in cybersecurity insurance as means of transferring some of the cybersecurity risks associated with potential future breaches.This paper provides a model for selecting the optimal set of cybersecurity insurance policies by a firm, given a finite number of policies being offered by one or more insurance companies. The optimal set of policies for the firm determined by this selection model can (and often does) contain at least three areas of possible losses not covered by the selected policies (called the Non-Coverage areas in this paper). By considering sets of insurance policies with three or more Non-Coverage areas, we show that a firm is often better able to address the frequently cited problems of high deductibles and low ceilings common in today’s cybersecurity insurance marketplace. Our selection model facilitates improved risk-sharing among cybersecurity insurance purchasers and sellers. As such, our model provides a basis for a more efficient cybersecurity insurance marketplace than currently exists. Our model is developed from the perspective of a firm purchasing the insurance policies (or the risk advisors guiding the firm) and assumes the firm’s objective in purchasing cybersecurity insurance is to minimize the sum of the costs of the premiums associated with the cybersecurity insurance policies selected and the sum of the expected losses not covered by the insurance policies.     

Equilibrium Pricing of General Insurance Policies

Abstract

A model is developed for determining the price of general insurance policies in a competitive, noncooperative market. This model extends previous single-optimizer pricing models by supposing that each participant chooses an optimal pricing strategy. Specifically, prices are determined by finding a Nash equilibrium of an N-player differential game. In the game, a demand law describes the relationship between policy sales and premium, and each insurer aims to maximize its (expected) utility of wealth at the end of the planning horizon. Two features of the model are investigated in detail: the effect of limited total demand for policies, and the uncertainty in the calculation of the breakeven (or cost price) of an insurance policy.

It is found that if the demand for policies is unlimited, then the equilibrium pricing strategy is identical for all insurers, and it can be found analytically for particular model parameterizations. However, if the demand for policies is limited, then, for entrants to a new line of business, there are additional asymmetric Nash equilibria with insurers alternating between maximal and minimal selling. Consequently it is proposed that the actuarial cycle is a result of price competition, limited demand, and entry of new insurers into the market. If the breakeven premium is highly volatile, then the symmetric equilibrium premium loading tends to a constant, and it is suggested that this will dampen the oscillatory pricing of new entrants.     

Weighted utility optimization of the participating endowment contract

ABSTRACT

In a participating endowment contract, the special loss compensation and profit sharing mechanism leads to heterogeneous benchmarks to distinguish the gain and loss for the policyholder's and the insurance company's S-shaped utilities. Because of the intense competition among the insurance companies and the requirement of the regulators, the benefits of the policyholders should be considered. As such, choosing the weighted utility of the two counterparts as the optimization objective is a rational setting. This setting induces a non-HARA (hyperbolic absolute risk aversion) and non-concave objective utility whose exact concavity and convexity are unknown. The difficulties not only come from this highly non-concave optimization problem, but also exist in the implicit integration of the optimum when solving the expected utilities of the two counterparts. We originally design an identification method to establish two categories of concave envelopes to solve the optimization problem, and propose an innovative numerical integration by substitution technique to deal with the implicit integration problem. The numerical simulation results recognize the existence of Pareto improvement of the two counterparts, which shows that the utilities of the policyholder and the insurance company can be simultaneously improved by switching into the weighted objective and appropriately amending the contract.     

Overview of Reserving Practices for Substandard Life Policies

Abstract

This paper reviews the various industry practices, both past and current, for determining statutory reserves for substandard life insurance policies This review begins with single-life policies but also considers the application of single-life practice to joint-life policies The increased popularity of joint-life policies has taken place without much discussion in the technical journals of how to handle such issues as reserves on substandard business. This paper is intended to provoke such a discussion and to provide a framework for it.     

A credibility theory for automobile bonus systems

Summary

This paper deals with the problem of designing experience rating systems of the bonus type, commonly used in automobile insurance. On the basis of a simple model the mean squared deviation between a policy's expected claim amount and its premium in the nth insurance period as n→∞, is taken as a measure of the efficiency of a bonus system. It is shown that to any set of bonus rules (which determines the bonus class transitions of the policies), there is an optimal premium scale, which coincides with the one proposed by Pesonen in 1963. Thus the problem of choosing an efficient bonus system reduces to choosing efficient bonus rules. Examples are given of comparison between different bonus rules. In one example the present Norwegian bonus system is compared to alternative systems. Comments are made on earlier papers on bonus systems. The credibility theoretic foundation is laid in a separate section.     

Sickness experience of Framtiden

Abstract

Introduction.

Livförsäkringsbolaget Framtiden, ömsesidigt (the Life Insurance Co. “The Future”, Mutual), to the policyholders of which I have the honour of devoting my actuarial work, is a relatively new enterprise. It was founded in 1911. Its main work is industrial life insurance with monthly premiums. All industrial policies include the waiver of premiums on disablement by sickness or accident for at least four weeks. Disablement lasting more than four weeks involves the waiver of premiums from the beginning of the disablement. For industrial policies issued in late years, the payment of premiums is limited to 65 years of age. Besides ordinary endowment (or whole life) policies, many childrens' insurances are written, including some or other insurance of the bread-winner, at all events the waiver of premiums till the 20th birthday of the child, if the supporter should die before that time, and for the periods during this time when the supporter is disabled by sickness or accident for at least four weeks. It has been tried to propagate more protective forms of children's policies, but it has partly failed, owing to lack of interest from agents and public. Nevertheless, it has been possible to exclude pure childrens' tariffs, and so in almost every policy issued, there is a moment of sickness insurance. In late years, this holds true also for the ordinary branch. The mass of experience collected is thus by no means unimportant, despite the smallness of the Company, as compared with foreign Companies. The experience is, moreover, collected during a relatively short period of time, giving a rather homogeneous material.     

Optimal insurance contracts without the non-negativity constraint on indemnities: revisited

In the literature on optimal indemnity schedules, indemnities are usually restricted to be non-negative. Keeler [1974] and Gollier [1987] show that this constraint might well bind: insured could get higher expected utility if insurance contracts would allow payments from the insured to the insurer at some losses. This paper extends Collier’s findings by allowing for negative indemnity payments for a broader class of insurers’ cost functions and argues that the indemnity schedule derived here is more appropriate for practical applications (e.g. in health insurance). JEL Classification D80 · D81 · D89