Axis Specialty, the Bermuda-based operation headed by John Charman, is to raise up to $517.5m (£322m) with a New York listing.
It revealed plans for an initial public offering in a filing with the US regulator, the Securities and Exchange Commission, last week.
It did not disclose how many shares would be sold or at what price they would be offered.
If the IPO plan goes ahead, Axis would be following fellow Bermudians Endurance Specialty, Montpelier Re and Platinum Underwriters, the former reinsurance arm of St Paul Companies.
The money raised would be used for general corporate purposes, the company said.
Axis shareholders include Blackstone Management Associates and JP Morgan Partners, each of whom hold a 10.1% stake, and Marsh & McLennan, which holds 6.5%.