Time Deductibles as Screening Devices: Competitive Markets

Seminal papers on asymmetric information in competitive insurance markets, analyzing the monetary deductible as a screening device, show that any existing equilibrium is of a separating type. High risks buy complete insurance, whereas low risks buy partial insurance—and this result holds for the Nash behavior as well as for the Wilson foresight. In this article, we analyze the strength of screening based on limitations to the period of coverage of the contract. We show that in this case (1) the Nash equilibrium may entail low risks not purchasing any insurance at all, and (2) under the Wilson foresight, a pooling equilibrium may exist.     

Equilibrium in Competitive Insurance Markets Under Adverse Selection and Yaari's Dual Theory of Risk

Under Yaari's dual theory of risk, we determine the equilibrium separating contracts for high and low risks in a competitive insurance market, in which risks are defined only by their expected losses, that is, a high risk is a risk that has a greater expected loss than a low risk. Also, we determine the pooling equilibrium contract when insurers are assumed non-myopic. Expected utility theory generally predicts that optimal insurance indemnity payments are nonlinear functions of the underlying loss due to the nonlinearity of agents' utility functions. Under Yaari's dual theory, we show that under mild technical conditions the indemnity payment is a piecewise linear function of the loss, a common property of insurance coverages.     

Screening equilibria in experimental markets

We conduct an experimental test of a screening model of an insurance market with asymmetric information. We first conduct three sessions in which the proportion of high risk buyers is such that a separating equilibrium should exist. We then conduct three more sessions in which the only change we make is decreasing the proportion of high risks such that the equilibrium is now a pooling equilibrium. In both treatments, the observed behavior converges to the equilibrium prediction.

The design of an optimal insurance contract for irreplaceable commodities

This paper discusses optimal insurance contract for irreplaceable commodities. To describe the dual impacts on individuals when a loss occurs to the insured irreplaceable commodities, we use a state-dependent and bivariate utility function, which includes both the monetary wealth and sentimental value as two arguments. We show that over (full, partial) insurance is optimal when a decrease in sentimental value will increase (not change, decrease, respectively) the marginal utility of monetary wealth. Moreover, a non-zero deductible exists even without administration costs. Furthermore, we demonstrate that a positive fixed reimbursement is optimal if (1) the premium is actuarially fair, (2) the monetary loss is a constant, and (3) the utility function is additively separable and the marginal utility of money is higher in the loss state than in the no-loss state. We also characterize comparative statics of fixed-reimbursement insurance under an additively separable preference assumption. JEL Classification G22 · D86 The author acknowledge funding from National Science Council in Taiwan (NSC93-2416-H-130-020).     

Complete Versus Incomplete Insurance Contracts under Adverse Selection with Multiple Risks

This article extends the standard adverse-selection model for competitive insurance markets, which assumes a single source of risk, to the case where individuals are subject to multiple risks. We compare the following market situations—the case where insurers can offer comprehensive policies against all sources or risks (complete contracts) and the case where different risks are covered by separate policies (incomplete contracts). In the latter case, we consider whether the insurer of a particular risk has perfect information regarding an individual's coverage against other sources of risks. The analysis emphasizes the informational role of bundling in multidimensional screening. When the market situation allows bundling, it is shown that in equilibrium the low-risk type with respect to a particular source of risk does not necessarily obtain partial coverage against that particular risk.     

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.     

On the Role of Patience in an Insurance Market With Asymmetric Information

We analyze a two-period competitive insurance market that is characterized by the simultaneous presence of moral hazard and adverse selection with regard to consumer time preferences. It is shown that there exists an equilibrium in which patient consumers use high effort and buy an insurance contract with high coverage, whereas impatient consumers use low effort and buy a contract with low coverage or even remain uninsured. This finding may help to explain why the opposite of adverse selection with regard to risk types can sometimes be observed empirically.     

Background Uncertainty and the Demand for Insurance Against Insurable Risks

Theory suggests that people facing higher uninsurable background risk buy more insurance against other risks that are insurable. This proposition is supported by Italian cross-sectional data. It is shown that the probability of purchasing casualty insurance increases with earnings uncertainty. This finding is consistent with consumer preferences being characterized by decreasing absolute prudence.     

Competition and Insurance Twenty Years Later

We are honored to address the European Group of Risk and Insurance Economists and will take the opportunity to make some reflections on the rather uneasy relationship between insurance and competition. Economists generally prescribe competition as a solution for markets that do not work well. Competition allocates resources efficiently and encourages innovation and attention to what customers want. Insurance markets differ from most other markets because in insurance markets competition can destroy the market rather than make it work better. One of the dimensions along which insurance companies compete is underwriting—trying to ensure that the risks covered are “good” risks or that if a high risk is insured, the premium charged is at least commensurate with the potential cost. The resulting partitioning of risk limits the amount of insurance that potential insurance customers can buy. In the extreme case, such competitive behavior will destroy the insurance market altogether. A simple model illustrates.     

Corporate Insurance Strategy: The Case of British Petroleum

The authors provide a fundamental rethinking of how corporations should evaluate various kinds of risks and risk management solutions—a rethinking that leads to a major shift in British Petroleum's approach to insuring property and casualty losses, product liability suits, and other insurable events. Conventional corporate practice—and until the early 1990s (when this article was written) the longstanding policy of BP and most large oil companies—was to insure against large losses while self‐insuring against smaller ones. In this article, the authors explain why BP has chosen to go against the conventional wisdom and instead buy insurance for mainly smaller losses while self‐insuring larger ones. The BP decision came down to factors affecting the market supply of insurance as well as the corporate demand for it. On the demand side, the authors demonstrate that the primary source of demand for insurance by large public companies is not, as standard insurance textbooks assume, to transfer risk away from the corporation's owners. Because corporate stockholders and bondholders effectively manage the effects of such risks by diversifying their own portfolios, the corporate demand for insurance in BP's case stems from the insurers' comparative advantage in evaluating and monitoring BP's smaller risks and in processing claims. On the supply side, the authors explain why the capacity of insurance companies and markets to underwrite very large or highly specialized exposures—when compared to the industry expertise and financial resources of companies like BP—is quite limited, and likely to remain so. Since premiums would be experience‐rated and prior years' losses simply rolled into the following years' premiums, there would be no effective transfer of risk, and so no gain to BP from buying insurance.