Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/150180
Title:

# Optimal insurance with adverse selection

Authors:
Schlee, Edward
Year of Publication:
2012
Citation:
[Journal:] Theoretical Economics [ISSN:] 1555-7561 [Volume:] 7 [Year:] 2012 [Issue:] 3 [Pages:] 571-607
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.
Subjects:
Principal-agent model
monopoly insurance
common values
wealth effects
quantity discounts
JEL:
D82
Persistent Identifier of the first edition:
Document Type:
Article
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