According to this article in USAtoday, Harvey to be costliest natural disaster in U.S. history, estimated cost of $160 billion. Some excerpts:

Hurricane Harvey could be the costliest natural disaster in U.S. history with a potential price tag of $160 billion, according to a preliminary estimate from private weather firm AccuWeather.

This is equal to the combined cost of Hurricanes Katrina and Sandy, and represents a 0.8% economic hit to the gross national product, AccuWeather said.

As of the 6pm news today, FEMA Administration, Brock Long, said it may be years before the full cost of the storm is known.  That probably is realistic.  Whether or not the event sets a record, it surely is among the biggest and costliest in history.  The duration of the event probably is going to set a record.