Live Streaming Video Camera?
The JVC  GY-HM200 has live streaming capabilities - http://pro.jvc.com/prof/attributes/features.jsp?model_id=MDL102319.

I've never used that particular model (so have no personal experience of the live streaming functions) but I do use the 170 and it's a solid little camcorder with a great range of options (including shooting in 4K and at high speed - though not at the same time), it's fairly robust and delivers great quality for the price.