If you are operating one private jet the chances are that the Pilot will be expected to deal with the day to day running and that should be negotiated in the Pilots fee.
If you are operating a group of aircraft then a management fee could be added.
Really it is so fluid but supply and demand will dictate.
Many company owners who operate more than one aircraft have an operating company with the pilots hired as a seperate thing.
Many companies do not want to be seen to own the aircraft and lease back.
There really are so many variations