AIG’s No. 2 Is Fighting to Turn Around the House That Hank Built

American International Group Inc.’s Peter Zaffino drew a clear line ahead of his jump to the insurer almost three years ago.

“I didn’t want any advice,” Zaffino, AIG’s president, said in a rare sit-down interview. “I needed to see things for myself,” he added. “You just have to get underneath, business review after business review.”

Several executives have tried to fix AIG in the past decade, and opinions abound over what’s needed to restore the vaunted status the insurer once boasted. Zaffino left a lucrative spot at Marsh & McLennan Cos. to join a longtime mentor, Chief Executive Officer ...