Question about Jealousy in relationships?

Okk so this doesn't have to do with a relationship I'm in or anything, just for future reference. When jealousy starts to come between two people in a relationship, who's job is it to fix the problem? For instance, if a girls boyfriend was getting jealous and pissy that she had a crush on a singer and was she getting all giddy for his concert--would it be her problem to sort of not flaunt it in front of him--or would it be his problem to get over his insecurities, or a combination of both?