Several approaches if it is steel you could have a nut welded onto the stud , hopefully with the heat induced it will help un seize it when time to undo it.
You could mark it accurately and Center punch it and drill the stud out starting from a small drill and working you way up in sizes untill you get near the thread size and tap it out, easier said than done though.
Another option of drilling a smaller hole and tapping it with a left handed thread then wind a left handed bold in and hopefully wind the stud out.
I would resist using one of those stud extractor as if that breaks in a drilled hole than you will have a real pig of a job.
Hopefully someone else will add some wisdom.
Looking at that photo again is that stud plastic? If so I would get a selection of drills and get near to that thread size you should be able to pick it out of the threads.