Just use one of the multitude of dynamic dns providers.

Yep. They give you a little program that runs on your computer that checks your external IP address at frequent intervals and updates the DNS records when it changes. Better yet, some home routers have a configuration page where you can select among popular Dynamic DNS providers and then you don't need to run the proprietary program. My ISP-provided router (FiOS) has ZoneEdit in the list which I've used for years even before I had FiOS, so it was a nice surprise when I found it there. Just for sake of example here's a link: http://www.zoneedit.com/dynamicDNS.html

Some registrars even provide such a service for free (well, included in the annual registration fee), though look for reviews to see how reliable your registrar's is before trying it in anger.

Simplest solution: buy a static IP for home

Or, as others have stated, use one of the dynamic dns mapping services.