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Optimal Insurance in a Monopoly: Dual Utilities with Hidden Risk Attitudes
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Optimal Insurance in a Monopoly: Dual Utilities with Hidden Risk Attitudes

Mario Ghossoub, Bin Li and Benxuan Shi
ArXiv.org
arXiv
04/01/2025
DOI: 10.48550/arxiv.2504.01095
url
https://doi.org/10.48550/arxiv.2504.01095View
Preprint (Author's original) This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We consider a monopoly insurance market with a risk-neutral profit-maximizing insurer and a consumer with Yaari Dual Utility preferences that distort the given continuous loss distribution. The insurer observes the loss distribution but not the risk attitude of the consumer, proxied by a distortion function drawn from a continuum of types. We characterize the profit-maximizing, incentive-compatible, and individually rational menus of insurance contracts, show that equilibria are separating, and provide key properties thereof. Notably, insurance coverage and premia are monotone in the level of risk aversion; the most risk-averse consumer receives full insurance(𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 π‘Žπ‘‘ π‘‘β„Žπ‘’ π‘‘π‘œπ‘) ; the monopoly absorbs all surplus from the least-risk averse consumer; and consumers with a higher level of risk aversion induce a higher expected profit for the insurer. Under certain regularity conditions, equilibrium contracts can be characterized in terms of the marginal loss retention per type of consumer, and they consist of menus of layered deductible contracts, where each such layered structure is determined by the risk type of the consumer. In addition, we examine the effect of a fixed insurance provision cost on equilibria. We show that if the fixed cost is prohibitively high, then there will be no𝑒π‘₯ π‘Žπ‘›π‘‘π‘’gains from trade. However, when trade occurs, separating equilibrium contracts always outperform pooling equilibrium contracts, and they are identical to those obtained in the absence of fixed costs, with the exception that only part of the menu is excluded. The excluded contracts are those designed for consumers with relatively lower risk aversion, who are less valuable to the insurer. Finally, we characterize incentive-efficient menus of contracts in the context of an arbitrary type space.

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