# On the design of optimal health insurance contracts under ex post moral hazard

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## Abstract

We analyze the design of optimal medical insurance under ex post moral hazard, i.e., when illness severity cannot be observed by insurers and policyholders decide for themselves on their health expenditures. The trade-off 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 insurers’ 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.

## Keywords

Health insurance Contract Ex post moral hazard Optimal control## JEL Classification

D82 D86 G22 I13## Notes

### Acknowledgements

Pierre Picard gratefully acknowledges financial support from LabEX ECODEC.

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© International Association for the Study of Insurance Economics 2018