Assume

(1) To reinsure all or part of another insurer’s risk. (2) A risk management technique involving the retention of risk (e.g., self-insurance).
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To take over a risk the converse of cede.
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To accept from another insurer all or part of the risk of an insured loss.
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REINSURANCE: To accept an obligation to indemnify all or part of a ceding company’s insurance or reinsurance on a risk or exposure subject to the contract terms and conditions.

Assumed (or Contractual) Liability

This insurance protects the insured in the event a loss occurs for which he has assumed liability, express or implied, under a written contract. For example, under most construction agreements with a municipality, the contractor agrees to “hold the municipality harmless” for any accidents arising out of the job. Contractual Liability Insurance would thus protect the contractor from any loss for which the municipality would be liable in connection with the construction.