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The authors analyze optimal risk sharing arrangements when losses are observable by policyholders and insurers but not verifiable. The optimal contract to insure individual losses can be implemented through a standard insurance contract with a deductible where the policyholder bears all losses lower than the deductible and an upper limit that restricts the maximum payment to the policyholder. For a group of policyholders it is optimal to choose contracts with individual deductibles and a joint upper limit. Insurance brokers can play an important role in implementing these contracts.
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