Optimal insurance with adverse selection

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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 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 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.

Original languageEnglish (US)
Pages (from-to)571-607
Number of pages37
JournalTheoretical Economics
Issue number3
StatePublished - Sep 2012


  • Common values
  • Empirical tests for adverse selection
  • Monopoly insurance
  • Principal-agent model
  • Quantity discounts
  • Wealth effects

ASJC Scopus subject areas

  • Economics, Econometrics and Finance(all)


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