Optimal insurance with adverse selection

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,: Department of Economics, Arizona State University
,: Department of Economics, Arizona State University
Authors registered in the RePEc Author Service: Edward Schlee and Hector Chade

Theoretical Economics, 2012, vol. 7, issue 3

Abstract: We solve the principal-agent 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 \emph{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 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 \emph{backwards-S shaped} in the amount of coverage, first 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.

Keywords: Principal-agent model; monopoly insurance; common values; wealth effects; quantity discounts; empirical tests for adverse selection (search for similar items in EconPapers)
JEL-codes: D82 (search for similar items in EconPapers)
Date: 2012-10-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (31)

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Related works:
Working Paper: Optimal Insurance with Adverse Selection (2008)
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