Some carriers, like SAS, contract the FF programs to private companies. I believe Carlson-Wagon Lit has a division that operates incentive programs for carriers like SAS, and also manage them [WorldPerks]. They also handle hotel programs. Most others are internal branches of the airline's marketing departments. I don't believe BA has any ownership position in the Canadian/NAmerican version of Air Miles, other than licensing the name. It may have even bailed out of the UK company.