From the Godfather:
Michael: The Corleone family's thinking of giving up all its interests in the olive oil business and settling out here.
I'm not sure if I follow what he said correctly so I'd like to ask first if it even make sense. If so, what is the meaning of give up interests? The give up phrasal could mean to stop doing something that you do regularly or to stop thinking or believing something. But how it can be tied with interests?
I'd say We give up all our interests in <something> means that we have no interests in that <something>.