Of course you can. It's called an AS (autonomous system), I think all you need is an IP address range, a physical link to someone willing to peer with you (another AS), some hardware, some paperwork, etc; and bam you're your own ISP.

My company has set this up for one of our customers (I wasn't involved).

> all you need is an IP address range, a physical link to someone willing to peer with you (another AS), some hardware, some paperwork, etc; and bam you're your own ISP.

I'm pretty sure the connotation of "self-host" entails a strictly substantially smaller scope than starting your own ISP.

Finding someone willing to peer with you also defeats the purpose. You are still fundamentally dependent on established ISPs.