Asymmetric Information, Long-Term Care Insurance, and Annuities: The Case for Bundled Contracts

This article examines the markets for long-term care insurance and annuities when there is asymmetric information and there are costs of administering contracts. Individuals differ in terms of their risk aversion. Risk-averse individuals take more care of their health and are relatively high risk in the annuities market and relatively low risk in the long-term care insurance market. In the long-term care insurance market, both separating and partial-pooling equilibria are possible. However, in the stand-alone annuity market, only separating equilibria are possible. We show, consistent with the extant empirical research, that in the presence of administration costs the more risk-averse individuals may buy relatively more long-term care insurance and more annuity coverage. Under the same assumptions, we show that equilibria exist with bundled contracts that Pareto dominate the outcomes with stand-alone contracts and are robust to competition from stand-alone contracts. The remaining empirical puzzle is to explain why bundled contracts are such a small share of the voluntary annuity market.     

Explaining Insurance Policy Provisions via Adverse Selection

In this article, we show that common insurance policy provisions—namely, deductibles, coinsurance, and maximum limits–can arise as a result of adverse selection in a competitive insurance market. Research on adverse selection typically builds on the assumption that different risk types suffer the same size loss and differ only in their probability of loss. In this study, we allow the severity of the insurance loss to be random and, thus, generalize the results of Rothschild and Stiglitz [1976] and Wilson [1977]. We characterize the separating equilibrium contracts in a Rothschild-Stiglitz competitive market. By further assuming a Wilson competitive market, we show that an anticipatory equilibrium might be achieved by pooling, and we characterize the optimal pooling contract.     

Participating Insurance Contracts and the Rothschild-Stiglitz Equilibrium Puzzle

We extend the Rothschild-Stiglitz (RS) insurance market model with adverse selection by allowing insurers to offer either non-participating or participating policies, that is, insurance contracts with policy dividends or supplementary calls for premium. It is shown that an equilibrium always exists in such a setting. Participating policies act as an implicit threat that dissuades deviant insurers who aim to attract low-risk individuals only. The model predicts that the mutual corporate form should be prevalent in insurance markets where second-best Pareto efficiency requires cross-subsidisation between risk types.     

Financial Markets for Unknown Risks if Beliefs Differ

We consider a general equilibrium model with individual and collective risks. The article builds on a contribution by Chichilnisky and Heal, who show that contingent Arrow–Debreu equilibria can also be supported in economies with Arrow securities and mutual insurance contracts. However, they show this to be true in general only if beliefs are identical, a very restrictive assumption in the context of unknown risks. Moreover, they claim complete insurance in equilibrium to be impossible if beliefs are different. We show that even with different beliefs, firstly, complete insurance is possible in each statistical state, and secondly, contingent equilibrium can still be supported in economies with insurance and securities.     

Dynamic Insurance Contracts and Adverse Selection

We take a dynamic perspective on insurance markets under adverse selection and study a dynamic version of the Rothschild and Stiglitz model. We investigate the nature of dynamic insurance contracts by considering both conditional and unconditional dynamic contracts. An unconditional dynamic contract has insurance companies offering contracts where the terms of the contract depend on time, but not on the occurrence of past accidents. Conditional dynamic contracts make the actual contract also depend on individual past performance (such as in car insurances). We show that dynamic insurance contracts yield a welfare improvement only if they are conditional on past performance. With conditional contracts, the first‐best can be approximated if the contract lasts long. Moreover, this is true for any fraction of low‐risk agents in the population.     

Competitive Insurance Markets and Adverse Selection in the Lab

We provide an experimental analysis of competitive insurance markets with adverse selection. Our parameterised version of the lemons’ model of Akerlof in the insurance context predicts total crowding-out of low risks when insurers offer a single full insurance contract. The therapy proposed by Rothschild and Stiglitz consists of adding a partial insurance contract so as to obtain self-selection of risks. We test the theoretical predictions of these two models in two experiments. A clean test is obtained by matching the parameters of these experiments and by controlling for the risk neutrality of insurers and the common risk aversion of their clients by means of the binary lottery procedure. The results reveal a partial crowding-out of low risks in the first experiment. Crowding-out is not eliminated in the second experiment and it is not even significantly reduced. Finally, instead of the predicted separating equilibrium, we find pooling equilibria. The latter can be sustained because insureds who objectively differ in their risk level do not perceive themselves as being so much different.     

Hidden insurance in a moral‐hazard economy

We analyze the general equilibrium of an economy in which a competitive industry produces nonexclusive insurance services. The equilibrium is inefficient because insurance contracts cannot control moral hazard, and welfare can be improved by policies that reduce insurance by increasing its price above marginal cost. We discuss how insurance production costs that exceed expected claim payments interact with moral hazard in determining the equilibrium's inefficiency, and show that these costs can make insurance premia so actuarially unfair as to validate the standard first‐order conditions we exploit in our analysis.     

Capital Allocation for Insurance Companies—What Good IS IT?

In their 2001 Journal of Risk and Insurance article, Stewart C. Myers and James A. Read Jr. propose to use a specific capital allocation method for pricing insurance contracts. We show that in their model framework no capital allocation to lines of business is needed for pricing insurance contracts. In the case of having to cover frictional costs, the suggested allocation method may even lead to inappropriate insurance prices. Beside the purpose of pricing insurance contracts, capital allocation methods proposed in the literature and used in insurance practice are typically intended to help derive capital budgeting decisions in insurance companies, such as expanding or contracting lines of business. We also show that net present value analyses provide better capital budgeting decisions than capital allocation in general.     

Upfront payments and exclusion in downstream markets

Although upfront payments are often observed in contracts between manufacturers and retailers, little is known about their competitive effects or the role retailers play in securing them. In this article, we consider a model in which two competing retailers make take‐it‐or‐leave‐it offers to a common manufacturer. We find that upfront payments are a feature of equilibrium contracts, and in all equilibria, only one retailer buys from the manufacturer. These findings support the claims of small manufacturers who argue that they are often unable to obtain widespread distribution for their products because of upfront payments.     

The Design of Optimal Insurance Contracts: A Topological Approach

This article deals with the optimal design of insurance contracts when the insurer faces administrative costs. If the literature provides many analyses of risk sharing with such costs, it is often assumed that these costs are linear. Furthermore, mathematical tools or initial conditions differ from one paper to another. We propose here a unified framework in which the problem is presented and solved as an infinite dimensional optimization program on a functional vector space equipped with an original norm. This general approach leads to the optimality of contracts lying on the frontier of the indemnity functions set. This frontier includes, in particular, contracts with a deductible, with total insurance and the null vector. Hence, we unify the existing results and point out some extensions.     

A Reexamination of the Costs of Firm Commitment and Best Efforts IPOs

Ritter [14] documents that best efforts IPOs are, on average, more costly to issue than firm commitment IPOs. This paper explains the phenomenon. Two component costs of going public are analyzed: underpricing and underwriter compensation. The model, based on a disagreement about firm value between underwriters and issuers, shows that underpricing is higher for firms using best efforts contracts as these firms, on average, are more speculative. Underwriter compensation is hypothesized to be higher for firms using best efforts contracts because of the high costs of market making for these firms in the aftermarket and the high distribution costs associated with the high risk of a failed offer. Empirical tests strongly support the propositions.     

Full Insurance, Bayesian Updated Premiums, and Adverse Selection

In the classic Rothschild-Stiglitz model of adverse selection in a competitive environment, we analyse a no-claims bonus type contract (bonus-malus). We show that, under full insurance coverage, if the insurance company applies Bayes's rule to learn about client probability types over time and uses this information in premium calculations for contract renewals, then there exist conditions under which all client types strictly prefer the Bayesian updating contract to the classic Rothschild-Stiglitz separating equilibrium.     

Adverse selection when loss severities differ: First-best and costly equilibria

With information asymmetry between contracting parties, adverse selection may result. A separation may be achieved if low-risk types can signal their identity—for example, by selecting from a menu of price-quantity contracts. In such models, signaling is costly and solutions are, at best, second best. These models characterize risk types by differences in the probability, rather than in severity, of the costs they impose. However, when severity differences also are considered, first best solutions become feasible. We identify the circumstances in which costly separating equilibria prevail and those in which full-information equilibria can be attained.     

Arbitrage and Viability in Insurance Markets

Insurance markets are subject to transaction costs and constraints on portfolio holdings. Therefore, unlike the frictionless asset markets case, viability is not equivalent to absence of arbitrage possibilities. We use the concept of unbounded arbitrage to characterize viable prices on a complete and an incomplete insurance market. In the complete market, there is an insurance contract for every possible event. In the incomplete market, risk can be insured through proportional and excess of loss like insurance contracts. We show how the the structure of viable prices is affected by the portfolio constraints, the transaction costs, and the structure of marketed contracts.     

Multidimensional Screening in Insurance Markets with Adverse Selection

Bundled coverage of different losses and distinct perils, along with differential deductibles and policy limits, are common features of insurance contracts. We show that, through these practices, insurers can implement multidimensional screening of insurance applicants who possess hidden knowledge of their risks, and thereby reduce the externality cost of adverse selection. Competitive forces drive insurers to exploit multidimensional screening, enhancing the efficiency of insurance contracting. Moreover, multidimensional screening allows competitive insurance markets to attain pure strategy Nash equilibria over a wider range of applicant pools, resolving completely the Rothschild–Stiglitz nonexistence puzzle in markets where the perils space is sufficiently divisible.     

Natural Disaster Insurance and the Equity-Efficiency Trade-Off

This article investigates the role of private insurance in the prevention and mitigation of natural disasters. We characterize the equity‐efficiency trade‐off faced by the policymakers under imperfect information about individual prevention costs. It is shown that a competitive insurance market with actuarial rate making and compensatory tax‐subsidy transfers is likely to dominate regulated uniform insurance pricing rules or state‐funded assistance schemes. The model illustrates how targeted tax cuts on insurance contracts can improve the incentives to prevention while compensating individuals with high prevention costs. The article highlights the complementarity between individual incentives through tax cuts and collective incentives through grants to the local jurisdictions where risk management plans are enforced.     

Systemlücken im deutschen und europäischen Haftungs- und Schadensrecht

The european liability systems differ widely. The divergences arise in the liability systems themselves, the extent of compensation in relation to damaged property and personal injury claims and the costs of bringing about an action. It is particulary problematic that the person having suffered damages (could say: injured party) cannot insure an unforeseen event and in addition the (tortfeasor) wrongdoer will often have to bear the costs for his own damages.The essay develops a concept of compensation that aims to close the liability gaps through private insurance contracts. In the context of these insurance contracts it is possible to choose the preferred legal system. The european liability and compensation systems can be harmonized without straining the european legislator. Furthermore, the article goes on to show that class action is going to gain more importance in Europe.     

Flexible Spending Accounts and Adverse Selection

I model the interaction of flexible spending accounts (FSAs) and conventional insurance in a simple discrete loss setting with asymmetric information. I show that FSA availability can break a separating equilibrium, even when one would otherwise exist, because high-risk types might prefer the lower-coverage contract supplemented with FSA funds. In this case there may exist a Pareto-inferior separating equilibrium. It is also shown that FSA availability alters the optimal pooling contract. Employers can reduce coverage levels, raising expected utility for low-risk types, and can compensate high-risk types by offering supplemental FSA coverage. Thus, it is possible that FSAs strengthen pooling contracts.     

Insurance markets and unisex tariffs: is the European Court of Justice improving or destroying welfare?

We analyze the effects of mandatory unisex tariffs in insurance contracts, such as those required by a recent ruling of the European Court of Justice, on equilibrium insurance premia and equilibrium welfare. In a unified framework, we provide a quantitative analysis of the associated insurance market equilibria in both monopolistic and competitive insurance markets. We investigate the welfare loss caused by regulatory adverse selection and show that unisex tariffs may cause market distortions that significantly reduce overall social welfare.     

On the Possibility of Profitable Self-Selection Contracts in Competitive Insurance Markets

Several studies extend the Rothschild–Stiglitz model of competitive insurance contracting with adverse selection by incorporating additional dimensions of private information and conclude that some insurers may earn positive profit in a separating, self-selection equilibrium, provided each insurer is restricted to making a single contract offer. The main result of this article is that these profitable configurations are not sustainable when individual insurers can offer multiple contracts. It is also shown that the ability to offer multiple contracts overturns equilibria that have applicants from different risk classes pooled as well as those where profits are dissipated by a fixed entry cost.