What is a type of reinsurance in which the reinsurer can accept or reject any risk presented by an insurance company seeking reinsurance ?

Facultative insurance is reinsurance for a single risk or a defined package of risks. The ceding company (the primary insurer) is not compelled to submit these risks to the reinsurer, but neither is the reinsurer compelled to provide reinsurance protection. Each risk under a facultative contract is individually underwritten by the reinsurer. Agreement to provide reinsurance “facilitates” the primary insurer’s desire to write the business; without the reinsurance, the primary insurer may be unable to provide coverage for the agent.