First Officer reported a 'severe' wake turbulence encounter on descent into MIA in trail of a B747. Reporter stated they were not advised by ATC they were in trail of a heavy jet.

Narrative

On arrival to MIA we were in the decent passing through 10;500 ft. at 250kts when we experienced severe wake turbulence. There was convective activity in the area and all traffic was getting radar vectors/deviations; however we were in the clear in a big hole of clear air. When we hit the wake we rolled rapidly to the right and hit a bank angle of approx 35-50 degrees; maybe more. We experienced the roll and significant vertical turbulence. It all lasted about 5 seconds and we rolled the wings level. The white 'AP FAIL' CAS message was displayed and the autopilot would not reengage for the remainder of the flight. The pilot monitoring (PM) notified ATC that we hit wake turbulence and his reply was something to the effect of 'yeah; you're following a 747.' At no point during the descent were we following nor were we told that we were following a [Boeing] 747. We were on MIA approach frequency. We had told the passengers that due to the weather it may get bumpy so they were all secure and there were no reported injuries. We discussed the event with the passengers upon landing and they seemed to understand. The aircraft was written up for severe wake turbulence. If your going to put a heavy in front of any business jet; ATC needs to advise what is happening. We couldn't see the 747 nor could we tell by call sign (because they weren't using 'heavy') that we were following a heavy let alone a 747.