The electronic ballast operates at a high frequency. The ballast, the reflector, and the cord between them can act as an emmitter - an antennae. In this case I believe that you ballast is emmitting frequencies in the FM range, which the radio reciever is picking up. All electronic devices do this, which is why there are emmision standards that portable electronic equipment has to be built to, and why airlines demand all electronic equipment be turned off while the plane is taking off or landing.
To prevent your ballast from acting as an antennae you have to shield it - dampen the intensity of the radio waves being emmited. A shield is a metal enclosure surrounding the ballast components that has a connection to ground. Most electronic ballasts come in a metal enclosure. This metal enclosure must be attached to ground to act as a shield. Is your ballast in a metal enclosure? Have you attached the ground wire of the power cord to the enclosure? In addition, the metal reflector/housing for the lamp should be grounded. A ground conductor should run from the reflector/housing to the ballast enclosure. If the ballast enclosure and the reflector are not grounded, try grounding them and see if this resolves the issue.
Grounding your lighting system also helps prevent you from being shocked.
You can also try to filter out the noise at the reciever. A power line filter can be placed between the wall socket and the radio power cord. If the radio has a seperate antennae you may also be able to put a noise filter between the antennae and the radio reciever. But I would try shielding the source, first, myself.