Export blog when I’m not the admin

An old webhost is hosting our blog, and we have three authors. I don’t have the admin login to the site, since our host maintains it – I only have the author logins. Is there any way to export all the entries we’ve written so I can import them into our new blog?

I know WordPress has an export feature, but it’s only available (as far as I can tell) if you’re the site admin, not if you’re only an author.