Investment Securities - Other long-term investments (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	$ 1,622.7	$ 1,377.8
Asset Management (Kudu)
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	813.2	669.5
PassportCard/DavidShield
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	132.0	120.0
Elementum Holdings, L.P.
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	45.0	45.0
Other unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	37.0	34.4
Total unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	1,027.2	868.9
Private equity funds and hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	239.8	153.8
Bank loan fund
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	155.7	163.0
Lloyd’s trust deposits
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	117.8	113.8
ILS funds
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	49.4	51.9
Private debt investments
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	13.0	14.1
Other
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	$ 19.8	$ 12.3