☰Day to day, claims run through professional adjusters, either a third-party administrator (TPA) engaged for the program or, in fronted arrangements, the fronting carrier's claims operation, with the captive reimbursing per the reinsurance agreement. Your captive manager oversees the process: making sure claims are reported promptly, reserved accurately, and moved toward closure, since open claims cost more the longer they stay open.
The difference from commercial insurance is accountability. The adjusters work for a program you own, so coverage questions get resolved on the policy you wrote rather than argued against an insurer's incentive to deny. Payout timelines run on your schedule. You also control how claims get resolved: you choose the adjusters, counsel, and repair vendors, and you can decide to handle a claim right rather than take the cheapest path. You also see everything: every claim and reserve in your own data. That visibility is one of the advantages of ownership, because claims data you can actually study is what drives the loss control that improves the program year over year.