Invite yourself to new event of shared calendar

I want to create a new event in an shared calendar from another iCloud account AND want to invite myself (my private iCloud account) so that the event will show up also in my private calendar. When I create the event on another machine with the other iCloud account it works. I get an invitation on my personal computer and can accept it. BUT when I create the event on my personal computer in the shared calendar and invite myself, I will get no invitations. Other people I invite to this event will get the invitation. What can I do?