Salvatore Ligresti, the former chairman of Fondiaria-SAI, was placed under house arrest and Jonella and Giulia Maria Ligresti have been jailed.
His son, Gioacchino Paolo Ligresti, is believed to be in Switzerland and is officially considered on the run.
Police also arrested three ex-managers at the company.
The business daily Il Sole 24 Ore said the Turin prosecutor's office, which is leading the investigation, suspects the people arrested hid important information from investors in the company.
The company had concealed €600 million in losses, the report quotes prosecutors as saying, which could have impacted 12,000 savers.
Fondiaria-SAI is also being targeted by a second investigation by the Milan prosecutor's office.
Ligresti had previously been convicted of corruption after a wave of investigations in the early 1990s.