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On the Design of Optimal Health Insurance Contracts under Ex Post Moral Hazard

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  • Pierre Martinon

    (Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems - CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en Automatique)

  • Pierre Picard

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris)

  • Anasuya Raj

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris)

Abstract

We analyze the design of optimal medical insurance under ex post moral haz- ard, i.e., when illness severity cannot be observed by insurers and policyholders decide for themselves on their health expenditures. The trade-o¤ between ex ante risk sharing and ex post incentive compatibility is analyzed in an optimal revelation mechanism under hidden information and risk aversion. The optimal contract provides partial insurance at the margin, with a deductible when in- surers' rates are affected by a positive loading, and it may also include an upper limit on coverage. The potential to audit the health state leads to an upper limit on out-of-pocket expenses.

Suggested Citation

  • Pierre Martinon & Pierre Picard & Anasuya Raj, 2018. "On the Design of Optimal Health Insurance Contracts under Ex Post Moral Hazard," Post-Print hal-01348551, HAL.
    • Handle: RePEc:hal:journl:hal-01348551
    DOI: 10.1057/s10713-018-0034-y
    Note: View the original document on HAL open archive server: https://polytechnique.hal.science/hal-01348551v3
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    References listed on IDEAS

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    Cited by:

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    3. Sun, Huan & Wang, Haiyan, 2024. "Data-driven incentive mechanism design for chronic disease prevention from the perspective of government," European Journal of Operational Research, Elsevier, vol. 313(2), pages 652-668.
    4. Peng Yang & Zhiping Chen, 2023. "Optimal Private Health Insurance Contract towards the Joint Interests of a Policyholder and an Insurer," Mathematics, MDPI, vol. 11(10), pages 1-28, May.

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    More about this item

    Keywords

    optimal control; health insurance; ex post moral hazard; audit; background risk;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • I13 - Health, Education, and Welfare - - Health - - - Health Insurance, Public and Private

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