You have the name of the chief executive? Write to him on paper with a stamp and tell him that his company is causing yours a nuisance. Say that under the provisions of statute X (whatever that may be in your country) you are entitled to claim compensation under the civil tort of harassment, or equivalent in your country. Enclose a copy of the relevant page of the legislation. There's sure to be plenty of legislation to choose from, take your pick. Enclose some printouts of the firewall warning messages.
That CEO will have to cancel his game of golf. He will be furious about that. He doesn't want to think about tiresome technology matters. He wants to think about golf. Above all, he must avoid the electric fence and not have any silly legal troubles. He will bang some heads together and the port scans will stop.
Someone asked me about receiving automated renewal reminders by email for an antivirus program he had ordered in error and then cancelled. He had asked not to receive such reminders anymore but they kept coming. The above steps worked for me.