The filing alleges Mr Davison's tweets were commented on, retweeted or reacted to by a number of his followers, creating a "grapevine effect".
In another tweet on April 24 this year, he wrote that Mr Kumova "certainly knows when to buy and sell a stock he is intimately connected with".
In a series of tweets in June he falsely accused Mr Kumova of being part of a pump-and-dump "syndicate".
In the statement of claim, Mr Kumova lists prominent journalists who follow the @stockswami account including from The Australian Financial Review, ABC, The Age and The Sydney Morning Herald, although he doesn't single them out for retweeting the posts.
"By reason of the publication by Davison of the matters complained of, Kumova has been brought into hatred, ridicule and contempt and has been gravely injured in his reputation including his professional reputation as a trader and mining executive and has suffered and will continue to suffer loss and damage," the statement of claim says.
Kumova is seeking aggravated damages against Davison due to the "ongoing" nature of the campaign, his "failure to inform Kumova of the imputations he intended to publish before publishing", and his "failure to publish an apology and retraction once informed of the factual errors" by Mr Kumova's lawyers.
Davison has previously discussed on his Twitter account how he became wealthy with an online business driving traffic to adult websites.
"I feel forever blessed and grateful for my luck," he tweeted in May. "It allowed me to raise my children while at home. It also allows me to sit here and disrupt the pump groups and ASX professional operators."
He also claims to have made $NZ1 million trading shares on the ASX.
"Cyber-bullying and online harassment cause great harm to many people," Mr Kumova said in a statement on Sunday.
"It is never OK, but it is particularly harmful when spewed anonymously from behind a keyboard. I have commenced legal action in the Federal Court to defend myself in the face of an online campaign by an anonymous social media troll."
Kumova said many people were "not in the position to be able to take on an international legal case".
"I am, and I have decided to do so because it is the right thing to do," he said. "Enough is enough."
Davison on Sunday tweeted, "I have in the last few days received a statement of claims that I made imputations that Tolga Kumova has engaged in inside trading. Let me be clear. That was not and has ever been my intention, inference or thought. I apologise to Tolga for any hurt caused."
He is yet to file a defence.
The matter will be heard in the NSW Federal Court by Justice Geoffrey Flick and is listed for mention on September 30.
- News.com.au