Revenues - Schedule of Operating Revenues by Geographic Area (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Jun. 30, 2025	Jun. 30, 2024	Jun. 30, 2025	Jun. 30, 2024
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	$ 2,064.0	$ 2,122.9	$ 6,427.0	$ 6,266.8
Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	1,640.8	1,689.9	5,113.7	5,056.0
Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	351.9	358.3	1,092.3	1,013.0
Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	59.9	61.8	185.3	162.3
Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	11.4	12.9	35.7	35.5
United States [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	1,553.9	1,596.4	4,846.7	4,706.5
United States [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	1,240.9	1,273.7	3,874.7	3,819.8
United States [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	249.9	256.8	776.2	718.8
United States [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	52.0	53.2	160.8	136.8
United States [Member] \| Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	11.1	12.7	35.0	31.1
Luxembourg [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	308.8	311.0	947.3	904.7
Luxembourg [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	214.2	216.2	654.0	630.1
Luxembourg [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	87.1	86.7	270.1	250.3
Luxembourg [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	7.5	8.1	23.2	23.6
Luxembourg [Member] \| Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.0	0.0	0.0	0.7
Asia-Pacific [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	82.4	77.2	242.2	229.7
Asia-Pacific [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	76.6	71.8	223.9	210.2
Asia-Pacific [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	5.2	4.7	16.5	14.3
Asia-Pacific [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.4	0.5	1.2	1.8
Asia-Pacific [Member] \| Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.2	0.2	0.6	3.4
Americas Excluding United States [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	58.9	69.2	181.4	203.5
Americas Excluding United States [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	49.5	59.1	152.3	173.8
Americas Excluding United States [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	9.4	10.1	29.0	29.6
Americas Excluding United States [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.0	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	60.0	69.1	209.4	222.4
Europe, Middle East and Africa, Excluding Luxembourg [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	59.6	69.1	208.8	222.1
Europe, Middle East and Africa, Excluding Luxembourg [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.3	0.0	0.5	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	$ 0.1	$ 0.0	$ 0.1	$ 0.3