Twitter User Wario64 pointed something out with a tweet:

This indicates that Crash Remastered while will be worked on by Sony Interactive Entertainment, this confirms that Activision likely owns the IP still and that they will have a role in the games production.
Their is likely a lot more to this story then announced now, so we will comment on the news as it comes out. The most important thing is that Crash is back, and with Sony/PlayStation backing this, it will end up being a great product in the long run.
Source: Twitter Post

UPDATE: Another thing worth noting is that Vicarious Visions will be making this remaster project. This is interesting, considering they are not making the Skylanders title this year (Toys For Bob are making that game) and they had history with Crash producing Nitro Kart and a number of Game Boy Advance titles in the series.
Source: Sony Interactive Entertainment Press Release

In addition to the wealth of content coming from SIE’s WWS, partnerships with the industry’s leading developers and publishers will further solidify PS4 as the best place to play for gamers.  At the press conference, SIEA announced it has worked with Activision to bring back one of PlayStation’s fan favorite characters, Crash Bandicoot.  Coming to PS4 first this October, Crash appears in Skylanders® Imaginators, the latest game from one of the most beloved franchises.  Additionally, in 2017, fans can play Crash 1, Crash 2, and Crash Warped, fully remastered for PS4 by Activision and Vicarious Visions.