This document is still a work in progress!
It is of course possible to run your own XMPP server. Here you will find some options for doing this with minimal effort:
YunoHost is an operating system aiming for the simplest administration of a server, in order to democratize self-hosting. It comes with a pre-installed XMPP server alongside other easy to install software for your server.
If you prefer something in-between a managed service and running your own server or VPS, Uberspace has you covered. They provide a detailed tutorial how to run your own Prosody XMPP service on their shared server.