Optimal insurance with adverse selection

• 成果类型: Article
• 署名作者: Chade, Hector; Schlee, Edward
• 署名单位: Arizona State University; Arizona State University-Tempe
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE671
• 发表日期: 2012-09-01
• 页码: 571-607
• 关键词: Principal-agent model; monopoly insurance; common values; wealth effects; quantity discounts; empirical tests for adverse selection; D82

摘要

We solve the principalagent problem of a monopolist insurer selling to an agent whose riskiness (loss chance) is private information, a problem introduced in Stiglitz's (1977) seminal paper. For an arbitrary type distribution, we prove several properties of optimal menus, such as efficiency at the top and downward distortions elsewhere. We show that these results extend beyond the insurance problem we emphasize. We also prove that the principal always prefers an agent facing a larger loss and prefers a poorer one if the agent's risk aversion decreases with wealth. For the standard case of a continuum of types and a smooth density, we show that, under the mild assumptions of a log-concave density and decreasing absolute risk aversion, the optimal premium is backward-S-shaped in the amount of coveragefirst concave, then convex. This curvature result implies that quantity discounts are consistent with adverse selection in insurance, contrary to the conventional wisdom from competitive models.