It is theoretically possible if you registered with a 'dynamic DNS' service to point to your IP regardless of whether it changed.
There are so many reasons why it wouldn't work well, but I think security is the most compelling. As soon as a computer is out on the internet for any length of time, it will get scanned, and even with industrial strength precautions it will get hit. If this is your own computer, all the files will become available to the first hacker that chances on it.
This doesn't even begin to address the technical reasons why this may not be the best idea.