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A general model of insurance under adverse selection

Author

Listed:
  • Michael Landsberger

    () (Department of Economics, Haifa University, Haifa 31905, ISRAEL)

  • Isaac Meilijson

    () (School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, ISRAEL)

Abstract

This paper considers optimal insurance schemes in a principal-agent multi-dimensional environment in which two types of risk averse agents differ in both risk and attitude to risk. Risk corresponds to any pair of distribution functions (not necessarily ordered by any of the usual dominance relations) and attitudes to risk are represented by any pair of non-decreasing and concave utility functions (not necessarily ordered by risk aversion). Results obtained in one-dimensional models that considered these effects separately and under more restricted conditions, are preserved in the more general set-up, but some of the questions we study can only be posed in the more general framework. The main results obtained for optimal insurance schemes are: (i) Insurance schemes preserve the order of certainty equivalents; consequently, the latter constitute a one-dimensional representation of types. (ii) Agents with the lower certainty equivalent are assigned full insurance. Partial insurance assigned to the others may entail randomization. (iii) Partially insured positions are an increasing function of the ratios of the probabilities that the two types assign to the uninsured positions. Most of these properties are preserved when, due to competition or other reasons, the insured certainty equivalents can not be set below pre-determined levels.

Suggested Citation

  • Michael Landsberger & Isaac Meilijson, 1999. "A general model of insurance under adverse selection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 331-352.
  • Handle: RePEc:spr:joecth:v:14:y:1999:i:2:p:331-352
    Note: Received: January 13, 1998; revised version: October 10, 1998
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    Citations

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    Cited by:

    1. Alma Cohen & Liran Einav, 2007. "Estimating Risk Preferences from Deductible Choice," American Economic Review, American Economic Association, vol. 97(3), pages 745-788, June.
    2. Pierre‐André Chiappori & Bruno Jullien & Bernard Salanié & François Salanié, 2006. "Asymmetric information in insurance: general testable implications," RAND Journal of Economics, RAND Corporation, vol. 37(4), pages 783-798, December.
    3. Carlier, G. & Dana, R.-A., 2005. "Rearrangement inequalities in non-convex insurance models," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 483-503, August.
    4. Cheung, Ka Chun & Dhaene, Jan & Lo, Ambrose & Tang, Qihe, 2014. "Reducing risk by merging counter-monotonic risks," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 58-65.
    5. James A. Ligon & Paul D. Thistle, 2008. "Adverse Selection With Frequency and Severity Risk: Alternative Risk-Sharing Provisions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(4), pages 825-846.
    6. Sandroni, Alvaro & Squintani, Francesco, 2013. "Overconfidence and asymmetric information: The case of insurance," Journal of Economic Behavior & Organization, Elsevier, vol. 93(C), pages 149-165.
    7. repec:dau:papers:123456789/5370 is not listed on IDEAS
    8. Andreas Richter & Jörg Schiller & Harris Schlesinger, 2014. "Behavioral insurance: Theory and experiments," Journal of Risk and Uncertainty, Springer, vol. 48(2), pages 85-96, April.
    9. repec:dau:papers:123456789/5389 is not listed on IDEAS
    10. repec:dau:papers:123456789/5358 is not listed on IDEAS

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