Just a few years ago, the Abbar family of Saudi Arabia could point to at least $383 million in investments managed by Citigroup Inc. Patriarch Abdullah Abbar and his son Ghazi had built the family fortune through an array of food import, travel, oil transport, and investment businesses. And beginning in 2006, they entrusted the bulk of their wealth to Citi.

Today the relationship has soured, and the money is almost gone. Both sides have lawyered up—the Abbars hired John Rich of Rich, Intelisano & Katz, and Citi retained Scott Edelman of Milbank, Tweed, Hadley & McCloy—and the legal battle is heating up. In August the Abbars filed a securities arbitration claim with the Financial Industry Regulatory Authority ­(FINRA), the U.S. securities industry’s self-regulator. But while defendants often prefer the privacy arbitration affords, Citigroup wants to move the case into the courtroom.