I have an applet, and it consist of an EXIT button which closes the applet.
Once the user clicks on the EXIT button, I would like to redirect to the user's
homepage or to a blank screen. I do not want to create this blank screen using HTML.
Why are you calling exit in an applet? That is contrary to the user web experience. A more appropriate thing to do would be to "logout" the user.
Check out AppletContext#showDocument() method(s) on how to display a particular page from an applet.