Revenues - Schedule of Operating Revenues by Geographic Area (Details) - USD ($) $ in Millions	3 Months Ended
Dec. 31, 2024	Dec. 31, 2023
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	$ 2,251.6	$ 1,991.1
Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	1,799.3	1,652.2
Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	375.5	296.4
Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	63.5	32.5
Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	13.3	10.0
United States [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	1,696.7	1,499.5
United States [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	1,361.4	1,260.6
United States [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	267.1	205.7
United States [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	55.1	24.2
United States [Member] \| Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	13.1	9.0
Luxembourg [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	325.3	276.3
Luxembourg [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	223.9	191.7
Luxembourg [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	93.4	76.5
Luxembourg [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	8.0	7.6
Luxembourg [Member] \| Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.0	0.5
Asia-Pacific [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	81.3	73.9
Asia-Pacific [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	75.8	68.5
Asia-Pacific [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	4.9	4.6
Asia-Pacific [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.4	0.6
Asia-Pacific [Member] \| Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.2	0.2
Americas Excluding United States [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	63.6	61.2
Americas Excluding United States [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	53.6	51.5
Americas Excluding United States [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	10.0	9.6
Americas Excluding United States [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.0	0.1
Americas Excluding United States [Member] \| Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.0	0.0
Europe, Middle East and Africa, Excluding Luxembourg [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	84.7	80.2
Europe, Middle East and Africa, Excluding Luxembourg [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	84.6	79.9
Europe, Middle East and Africa, Excluding Luxembourg [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.1	0.0
Europe, Middle East and Africa, Excluding Luxembourg [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.0	0.0
Europe, Middle East and Africa, Excluding Luxembourg [Member] \| Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	$ 0.0	$ 0.3