web app – Should a Notification Center have an infinite history or should it allow the user to close them?

I’m working on a Notification Center (in a web application) and I can’t find any information about the notifications history.

So I don’t know what is the best behaviour to apply for my notification center.

Example: Facebook and Pinterest have an infinite history.

  • Should I keep all the notifications in history, in which context?
  • Should I allow the user to close the notifications, in which context?

For more context, I’m working on a Financial Application for Advisors.
So there is no “Messages notifications”, the notifications we’ll find in the Notification Center will be more like “There are new alternatives available in your comparison #1”. The notification will redirect the user to the source.

Here’s my sources for the notifications: