Are any agile (aerobatic) private jets produced?
The reason these aren't built is that there's no market for them. Sure, there's loads of people who would love one of these (including me) but they would be incredibly expensive to buy and operate, far out of reach for anyone but the extremely wealthy. 

At the airfield I fly from there are Jet Provosts, a 50's era jet trainer, available. These old, not particularly fast or agile jets cost about 1000 USD per  hour to fly. I've seen Mig-21 (certainly fast with lots of Gs) training for about $4500 per hour, which gives you an idea of the running costs for a fast, exciting jet. 

The existing market of people who can afford this is already supplied by military surplus jets. These run from trainers like the L-39 and Gnats to fighters and bombers like Migs, an F-104, hawker hunter, there's even a privately owned Harrier. These don't cost that much to buy considering what one would cost new, and there's plenty of them on the market, so there's no call for new builds.