Time, Risk, Precommitment, and Adverse Selection in Competitive Insurance Markets
Time, Risk, Precommitment, and Adverse Selection in Competitive Insurance Markets

Author: Mark V. Pauly

Publisher:

Published: 2003

Total Pages: 21

ISBN-13:

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This informal paper explores models of competitve insurance market equilibrium when individuals of initially similar apparent risk experience divergence in risk levels over time. The information structrue is modeled in three alternative ways: all insurers and insureds know risk at any point in time, current insurer and insured know risk, and only the individual knows risk. Insurers always know the average risk. It is shown that some models lead to "backloading" of premiums in which initial period expected expense, and that other models lead to "frontloading" of premiums and policy provisions of "guaranteed renewability." Finally, it is shown that guaranteed renewability greatly reduces the possibility of adverse selection.

Optimality and Equilibrium In a Competitive Insurance Market Under Adverse Selection and Moral Hazard
Optimality and Equilibrium In a Competitive Insurance Market Under Adverse Selection and Moral Hazard

Author: Joseph E. Stiglitz

Publisher:

Published: 2013

Total Pages:

ISBN-13:

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This paper analyzes optimal and equilibrium insurance contracts under adverse selection and moral hazard, comparing them with those under a single informational asymmetry. The complex interactions of self-selection and moral hazard constraints have important consequences. We develop an analytic approach that allows a characterization of equilibrium and optimal (Pareto Optimal (PO), and Utilitarian optimal (UO)) allocations. Among the results : (i) a PO allocation may involve "shirking" (not only less care in accident avoidance than is possible, but less care compared to the case of pure moral hazard) either by high risk individuals in the case of single-crossing preference or by one or both types in the case of multi-crossing preference (as may naturally be the case under the double informational asymmetry); and (ii) while an equilibrium, which is unique (even under multi-crossing preferences) if it exists, is more likely to exist as the non-shirking constraint for low-risk type gets more stringent (i.e. when low risk individuals shirk with lower levels of insurance). We also show that a pooling equilibrium, which is not feasible under pure adverse selection, may exist when individuals differ in risk aversion (as well as in accident probability) or when the provision of insurance is non-exclusive (i.e. individuals can purchase insurance from more than one firm). Furthermore, while with pure adverse selection, UO always entails pooling with complete insurance (in the standard model), with adverse selection and moral hazard, all PO allocations may entail separation and the UO may entail incomplete insurance. We show further that, in general, any PO allocation can be implemented by a basic pooling insurance provided by the government and a supplemental separating contracts that can be offered by the market, although, in the presence of moral hazard, a tax needs to be imposed upon the market provision. The analysis suggests that two commonly obser.

Existence of Equilibria in Competitive Insurance Markets
Existence of Equilibria in Competitive Insurance Markets

Author: Peter S. Faynzilberg

Publisher:

Published: 2006

Total Pages:

ISBN-13:

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Under the conditions conjectured by Rothschild and Stiglitz (1976)as leading to market failure, we demonstrate the existence of a uniqueequilibrium in a risk-sharing economy with adverse selection. This equilibrium may be separating or partially pooling: in an economy withthree types, for instance, the low- and the medium-risk buyer segmentsmay be offered the same insurance policy.In equilibrium, buyers' indirect utility decreases with their propensityfor accident. When low-risk buyers are prevalent, sellers subsidizetheir operations across segments: they derive a positive profit in thelow-risk segment and incur a loss of equal magnitude in the rest ofthe economy. This leaves high-risk buyers better off than under thefirst-best policy they purchase when sellers are perfectly informed.In contrast to the putative equilibrium of the Rothschild-Stiglitzmodel, the second-best equilibrium depends on the structure of thebuyer population and converges to the first-best of the correspondinghomogeneous population as low- risk buyers become increasingly prevalentin the economy.

Consumer Risk Perceptions and Information in Insurance Markets with Adverse Selection
Consumer Risk Perceptions and Information in Insurance Markets with Adverse Selection

Author: James A. Ligon

Publisher:

Published: 2008

Total Pages:

ISBN-13:

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Standard models of adverse selection in insurance markets assume policyholders know their loss distributions. This study examines the nature of equilibrium and the equilibrium value of information in competitive insurance markets where consumers lack complete information regarding their loss probabilities. We show that additional private information is privately and socially valuable. When the equilibrium policies separate types, policyholders can deduce the underlying probabilities from the contracts, so it is information on risk type, rather than loss probability per se, that is valuable. We show that the equilibrium is quot;as ifquot; policyholders were endowed with complete knowledge if, and only if, information is noiseless and costless. If information is noisy, the equilibrium depends on policyholders' prior beliefs and the amount of noise in the information they acquire.

Insurance Contracting with the Coexistence of Adverse Selection and Moral Hazard
Insurance Contracting with the Coexistence of Adverse Selection and Moral Hazard

Author: Zhiqiang Yan

Publisher:

Published: 2014

Total Pages: 40

ISBN-13:

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The asymmetric information problem has been widely discussed in the context of insurance markets. Most of previous research usually treats adverse selection and moral hazard separately, though it is quite possible that they may coexist and interact with each other. In this paper, we build a principal-agent model to examine optimal contracts in a competitive insurance market facing adverse selection and moral hazard simultaneously. We apply the change-of-variable method and the Kuhn-Tucker conditions to solve the optimization programs and find that there are several forms of separating Nash equilibria, although separating Nash equilibria may not exist. Our model brings richer equilibria and retains some properties in the benchmark models of pure adverse selection and pure moral hazard. For example, no agent is offered full insurance, and the positive correlation between insurance coverage and risk type still holds. Our study on comparative statics indicates that, under some conditions, the optimal indemnity and premium, in general, decrease with the disutility, increase with the potential loss and decrease with the intial wealth of the insured.