In his filing, Griffin said Dias is demanding money for her own lifestyle "under the guise" of the children's expenses.
He said those include $300,000 a month for private-jet travel, $160,000 a month for vacation rentals and $60,000 a month for office space and professional staff.
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In a statement, Dias said the filing is "riddled with falsehoods and just another vindictive attempt by Ken Griffin—Illinois' richest billionaire—to punish his family and avoid his clear responsibility under Illinois law to maintain his children's lifestyle."
Dias's statement doesn't dispute the dollar numbers. But she said Griffin is refusing to give the kids "the support to which they are accustomed and entitled under Illinois law."
Sources close to Dias say the nearly $1 million a month was not a demand by Dias, but an accounting of the couple's child-related expenses while they were married. If so, those expenses would likely be required to continue after the divorce under Illinois law.
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In the filing, Griffin said "it is clear that the only exigency Anne sees is the risk that she might have to start spending some of her own substantial wealth to support herself in the opulent lifestyle she desires."