A single-parent captive, also called a pure captive, is an insurance company owned by one business and formed to insure that business and its affiliates. It is the classic form: one owner, one balance sheet, full control over coverage, retention, and what happens to the surplus. Most of the large, mature captive programs in the world are single-parent captives.
The tradeoff is that all of it is yours: the capital commitment, the governance, and the risk. That is why single-parent captives fit companies whose premium and loss history are substantial enough to carry their own insurance company, and why many owners arrive here by graduating from a cell or group structure once the program has proven itself.