Revenues - Schedule of Operating Revenues by Geographic Area (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Mar. 31, 2025	Mar. 31, 2024	Mar. 31, 2025	Mar. 31, 2024
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	$ 2,111.4	$ 2,152.8	$ 4,363.0	$ 4,143.9
Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	1,673.6	1,713.9	3,472.9	3,366.1
Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	364.9	358.3	740.4	654.7
Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	61.9	68.0	125.4	100.5
Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	11.0	12.6	24.3	22.6
United States [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	1,596.1	1,610.6	3,292.8	3,110.1
United States [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	1,272.4	1,285.5	2,633.8	2,546.1
United States [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	259.2	256.3	526.3	462.0
United States [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	53.7	59.4	108.8	83.6
United States [Member] \| Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	10.8	9.4	23.9	18.4
Luxembourg [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	313.2	317.4	638.5	593.7
Luxembourg [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	215.9	222.2	439.8	413.9
Luxembourg [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	89.6	87.1	183.0	163.6
Luxembourg [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	7.7	7.9	15.7	15.5
Luxembourg [Member] \| Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.0	0.2	0.0	0.7
Asia-Pacific [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	78.5	78.6	159.8	152.5
Asia-Pacific [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	71.5	69.9	147.3	138.4
Asia-Pacific [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	6.4	5.0	11.3	9.6
Asia-Pacific [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.4	0.7	0.8	1.3
Asia-Pacific [Member] \| Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.2	3.0	0.4	3.2
Americas Excluding United States [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	58.9	73.1	122.5	134.3
Americas Excluding United States [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	49.2	63.2	102.8	114.7
Americas Excluding United States [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	9.6	9.9	19.6	19.5
Americas Excluding United States [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.1	0.0	0.1	0.1
Americas Excluding United States [Member] \| Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.0	0.0	0.0	0.0
Europe, Middle East and Africa, Excluding Luxembourg [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	64.7	73.1	149.4	153.3
Europe, Middle East and Africa, Excluding Luxembourg [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	64.6	73.1	149.2	153.0
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	0.2	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	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	$ 0.0	$ 0.0	$ 0.3