The Merriam-Webster dictionary defines fan fiction as "stories involving popular fictional characters that are written by fans and often posted on the Internet - also called fan fic". Most works of fan fiction are generally obscene, insane, unrealistic and written with grammar ripped from a fifth grader. But really, that's just the point of fan fiction. It's basically, "Who the fuck cares, this is my work, I can make anything happen." And in fan fictions, anything is ANYTHING. Some fan fictions actually make the story better. The rest are just literary Rule 34.
Although writing fan fictions has been a favorite pastime for both writers and non-writers, writers of the genre usually have a very, very small reader base (i.e. himself). So what's the point of writing something that only you are willing to read? The whole situation could be a little better if you wrote a fan fiction about you instead.
While writing a fan fiction for oneself would violate the definition given above (you are no longer writing about a fictional character), it's a great way to escape the harsh view of reality. Say for example you made a mistake that fucked your life up good. You can write a fan fiction as a recount of that event, but instead of portraying yourself as a failure you can actually fix everything by rewriting it. It sort of like photoshopping a shitty photograph to make it better. Remove some key events, change how everything happened, maybe even throw Chuck Norris in as some sort of equalizer for that story of your life.
However, as amusing or awesome your self fan fiction will be, it would be best that you DO NOT publish it to be read by other people. Keep it somewhere confidential. Nobody really wants to read your fan fiction about fighting dragons part-time being the reason you are late at work everyday. And when they do, the consequences are almost always never the same.