The widest aperture native Micro 4/3 zoom lens is the Panasonic Leica 10-25mm f/1.7.
There are also several native f/2.8 aperture zoom lenses:
- Olympus 7-14mm f/2.8
- Panasonic 12-35mm f/2.8
- Olympus 12-40mm f/2.8
- Panasonic 35-100mm f/2.8
- Olympus 40-150mm f/2.8
None of these lenses have an especially wide zoom range (by the standards of broadcast video zoom lenses). Olympus makes a 12-100mm f/4.0 lens which has a decent range, but does not have an especially fast aperture.
Note that none of these lenses have power zoom capability. If you need that you are stuck with the four native Micro 4/3 power zoom lenses:
https://www.blackmagicdesign.com/support/faq/59009As Steve mentions, if you use a Speed Booster you can get an effective increase in f-stop from full-frame or even APS-C lenses. The best option for the Studio Camera 4K is probably the Super 16 (0.58x) Speed Booster which gives a boost of about 1 2/3 stops in light gathering. If you pair these with something like the Sigma 18-35mm f/1.8 or 50-100mm f/1.8 lenses, it will effectively turn them into f/1.0 zooms.