Influential Articles, Journals, and Institutions in Risk Management and Insurance

We use a threshold citation approach to measure the influence of articles, journals, and institutions in risk management and insurance research. The three frequently cited articles in risk management and insurance research are "Increasing Risk: I. A Definition" by Rothschild and Stiglitz (1970), "Precautionary Saving in the Small and in the Large" by Kimball (1990), and "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information" by Rothschild and Stiglitz (1990). Journal of Risk and Insurance, Econometrica, and Journal of Political Economy are the three influential journals in risk management and insurance research. Furthermore, the five influential institutions in risk management and insurance research are the University of Pennsylvania, Harvard University, the University of Rochester, the University of Michigan, and Massachusetts Institute of Technology.     

First-Best Equilibrium in Insurance Markets With Transaction Costs and Heterogeneity

We investigate extensions of the classic Rothschild and Stiglitz (1976) (RS) model of adverse selection under asymmetric information. In RS, low‐risk customers are worse off owing to an externality created by high‐risk buyers in the market. We find critical changes in insurance buyers' behavior under the joint assumptions of transaction costs and buyer heterogeneity with respect to either risk aversion or wealth. Combining transaction costs and heterogeneity, we find a separating equilibrium in which neither high‐risk nor low‐risk individuals are penalized due to information asymmetry.     

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.     

Unravelling vs Unravelling: A Memo on Competitive Equilibriums and Trade in Insurance Markets

Both Akerlof (1970) and Rothschild and Stiglitz (1976) show that insurance markets may “unravel”. This memo clarifies the distinction between these two notions of unravelling in the context of a binary loss model of insurance. I show that the two concepts are mutually exclusive occurrences. Moreover, I provide a regularity condition under which the two concepts are exhaustive of the set of possible occurrences in the model. Akerlof unravelling characterises when there are no gains to trade; Rothschild and Stiglitz unravelling shows that the standard notion of competition (pure strategy Nash equilibrium) is inadequate to describe the workings of insurance markets when there are gains to trade.     

A Reexamination of Credit Rationing in the Stiglitz and Weiss Model

We reexamine Stiglitz and Weiss (1981) credit rationing by simultaneously considering adverse selection and moral hazard. If returns of the projects are ranked by first‐order stochastic dominance, neither adverse selection nor moral hazard exists. If the projects have equalized expected returns, moral hazard does not exist, and credit rationing due to adverse selection occurs under extreme conditions. If the projects are ranked by second‐order stochastic dominance (SSD), adverse selection and moral hazard may coexist, logically restoring credit rationing, but SSD imposes strict limitations on lenders’ ability to classify borrowers. In general, our results do not support significance of credit rationing.     

Mossin's Theorem Given Random Initial Wealth

The purpose of this article is to reexamine Mossin's Theorem under random initial wealth. Conditions necessary and sufficient for Mossin's Theorem depend on the stochastic dependence between risks. The correlation coefficient, however, is not an adequate measure of stochastic dependence in the general expected‐utility model, and so other notions of dependence are used to investigate Mossin's Theorem. The inadequacy of the correlation coefficient is illustrated with two counterexamples. Then, using notions of positive and negative dependence measures, we provide necessary and sufficient conditions for a generalized Mossin Theorem to hold. In addition, a generalized Mossin Theorem is interpreted using the notion of a mean preserving spread made popular by Rothschild and Stiglitz (1970) . Given a fair premium and dependent stochastic conditions, we show that an individual can obtain a final wealth distribution with less weight in its tails by selecting less than or more than full insurance.     

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.     

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.     

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.     

Guaranteed renewable life insurance under demand uncertainty

Guaranteed renewability (GR) is a prominent feature in many health and life insurance markets. We develop a model that includes unpredictable (and unobservable) fluctuations in demand for life insurance as well as changes in risk type (observable) over individuals' lifetimes. The presence of demand type heterogeneity leads to the possibility that optimal GR contracts may have a renewal price that is either above or below the actuarially fair price of the lowest risk type in the population. Individuals whose type turns out to be high risk but low demand renew more of their GR insurance than is efficient due to the attractive renewal price. This results in imperfect insurance against reclassification risk. Although a first‐best efficient contract is not possible in the presence of demand type heterogeneity, the presence of GR contracts nonetheless improves welfare relative to an environment with only spot markets.     

Redistributive taxation and social insurance under adverse selection in the insurance market

This paper extends the analysis of optimal income taxation under uncertainty studied by Cremer and Pestieau (International Tax and Public Finance, 3, 281–295, 1996). We introduce asymmetric information in the insurance market whereby private insurance companies cannot identify the risk probability of the agents, and we examine its effect on public policy. We consider the separating equilibrium of Rothschild and Stiglitz (Quarterly Journal of Economics, 90, 629–649, 1976) and Riley (Econometrica, 47, 331–359, 1979) where the low risk agent is only partially insured. The presence of the distortion in the insurance market changes the affinity of labor, and in some cases, we show that the scope of redistribution and the resulting social welfare are higher under asymmetric information than under full information. We also show that the increase in social insurance affects the utility and labor incentive of the low risk type by relaxing the self-selection constraint in the insurance market. The policy implications of the redistributive taxation and social insurance are analytically and numerically examined.      

Stochastic Dominance and Conditional Expectation—An Insurance Theoretical Approach

We show that the relation of second order stochastic dominance, which has found widespread use in models of economic behavior under uncertainty, may be described in terms of conditional expectation. If a distribution G second order stochastically dominates another distribution F, then there are random variables g and f with distributions G and F, respectively, such that g can be obtained from f by iterated conditional expectation. In terms of insurance, this shows that the less risky distribution can be obtained by a sequence of insurance contracts each one insuring against the residual risk left over from the previous contracts.     

New Developments in the Theory of Adverse Selection in Competitive Insurance

We provide an overview of the paths taken to understand existence and efficiency of equilibrium in competitive insurance markets with adverse selection since the seminal work by Rothschild and Stiglitz (1976). A stream of recent work reconsiders the strategic foundations of competitive equilibrium by carefully modelling the market game.     

How does managed care do it?

Integrating the health services and insurance industries, as health maintenance organizations (HMOs) do, could lower expenditure by reducing either the quantity of services or unit price or both. We compare the treatment of heart disease in HMOs and traditional insurance plans using two datasets from Massachusetts. The nature of these health problems should minimize selection. HMOs have 30% to 40% lower expenditures than traditional plans. Both actual treatments and health outcomes differ little; virtually all the difference in spending comes from lower unit prices. Managed care may yield substantial increases in measured productivity relative to traditional insurance.     

Optimal Loss Mitigation and Contract Design

This work examines the interaction between the premium rates set by an insurer and the incentives of an individual to purchase market insurance and undertake mitigation to reduce the size of a potential loss. A risk‐neutral monopolistic insurer prices insurance according to the price‐elasticity of demand for coverage. The elasticity of demand is affected by the presence of both mitigation and government intervention. The availability of loss reduction activities increases the consumer's elasticity of demand and lowers the optimal rate charged by the monopolist. Government intervention reduces both expenditures on mitigation and the rate charged by the monopolistic insurer.     

Flood Insurance Coverage in the Coastal Zone

We explore determinants of flood insurance demand in the coastal zone using micro‐data for nine Southeastern counties. Overall estimates indicate price inelastic demand, though subsidized policyholders have greater coverage and are more price sensitive. Mortgage borrowers exhibit no greater coverage; only 12 percent in 100‐year flood zone indicate flood insurance was required by their lender. Flood insurance demand is increasing in the levels of flood and erosion risk. We find a positive correlation between household income and coverage, but the effect is not monotonic. Community‐level erosion hazard mitigation projects influence flood insurance coverage, with beach replenishment acting as a complement.     

Insurance demand in the presence of loss-dependent background risk

We analyze insurance demand when insurable losses come with an uninsurable zero-mean background risk that increases in the loss size. If the individual is risk vulnerable, loss-dependent background risk triggers a precautionary insurance motive and increases optimal insurance demand. Prudence alone is sufficient for insurance demand to increase in two cases: the case of fair insurance and the case where the smallest possible loss exceeds a certain threshold value (referred to as the large loss case). We derive conditions under which insurance demand increases or decreases in initial wealth. In the large loss case, prudence determines whether changes in the background risk lead to more insurance demand. We generalize this result to arbitrary loss distributions and find conditions based on decreasing third-degree Ross risk aversion, Arrow–Pratt risk aversion, and Arrow–Pratt temperance.     

The effect of overconfidence on insurance demand

The Geneva Risk and Insurance Review - Sandroni and Squintani (Am Econ Rev 97(5):1994–2004, 2007) argue that in the presence of overconfident agents, the findings of Rothschild and Stiglitz...     

经济政策不确定性、地区文化与保险需求

本文在拓展背景风险理论研究的基础上,揭示了经济政策不确定性对保险需求的影响及其受地区文化制约的理论机制。并利用2007-2017年中国30个地区的月度面板数据,检验了经济政策不确定性、地区文化与保险需求间的内在联系。结果发现:第一,经济政策不确定性会对保险需求产生显著正影响,且这种效应在地区人身险需求上表现更明显;第二,将地区文化指标集纳入经济政策不确定性与保险需求关系的研究框架,发现地区文化差异会对经济政策不确定性影响保险需求产生调节效应。因此政府需在充分重视经济政策波动和文化对经济活动的双重影响基础上,加强国内社会保障体系建设,建立更透明的信息传递渠道,培育人们主动抵抗风险的意识和文化习惯,调整保险供给结构,以减少不确定性对社会经济行为的负面冲击。     

Stochastic dominance as an approach to uncertainty in cost accounting

Presently textbook treatment of the topic of uncertainty in cost accounting never goes beyond the notions of mean and variance and the maximization of expected utilities. Because the application of these models requires artificial assumptions about either loss functions or utility functions, students are often left wondering how practical probabilistic models are afterall. This paper suggests that stochastic dominance be used to supplement the current textual material on uncertainty. Since these models are easy to implement in a cost accounting context, the class can devote more time to accounting issues in the context of uncertainty rather than get lost in decision theory. Three models of stochastic dominance are discussed here: the first order, the second order, and the third order stochastic dominance. All the necessary assumptions about each model are stated, and each model is accompanied by a numerical example.