Revenues - Schedule of Operating Revenues by Geographic Area (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Mar. 31, 2024	Mar. 31, 2023	Mar. 31, 2024	Mar. 31, 2023
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	$ 2,152.8	$ 1,927.2	$ 4,143.9	$ 3,894.3
Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	1,713.9	1,573.3	3,366.1	3,205.1
Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	358.3	301.4	654.7	593.3
Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	68.0	43.3	100.5	76.7
Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	12.6	9.2	22.6	19.2
United States [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	1,610.6	1,421.3	3,110.1	2,939.3
United States [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	1,285.5	1,165.8	2,546.1	2,440.6
United States [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	256.3	212.4	462.0	420.6
United States [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	59.4	34.6	83.6	59.9
United States [Member] \| Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	9.4	8.5	18.4	18.2
Luxembourg [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	317.4	278.3	593.7	536.2
Luxembourg [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	222.2	196.6	413.9	378.4
Luxembourg [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	87.1	73.6	163.6	142.0
Luxembourg [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	7.9	7.8	15.5	15.5
Luxembourg [Member] \| Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.2	0.3	0.7	0.3
Asia-Pacific [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	78.6	88.3	152.5	161.6
Asia-Pacific [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	69.9	82.5	138.4	150.1
Asia-Pacific [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	5.0	5.0	9.6	10.0
Asia-Pacific [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.7	0.7	1.3	1.1
Asia-Pacific [Member] \| Other [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	3.0	0.1	3.2	0.4
Americas Excluding United States [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	73.1	66.9	134.3	129.0
Americas Excluding United States [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	63.2	56.3	114.7	108.1
Americas Excluding United States [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	9.9	10.4	19.5	20.7
Americas Excluding United States [Member] \| Shareholder servicing fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.0	0.2	0.1	0.2
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	73.1	72.4	153.3	128.2
Europe, Middle East and Africa, Excluding Luxembourg [Member] \| Investment management fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	73.1	72.1	153.0	127.9
Europe, Middle East and Africa, Excluding Luxembourg [Member] \| Sales and distribution fees [Member]
Disaggregation of Revenue [Line Items]
Operating revenues by geographic area	0.0	0.0	0.0	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	$ 0.3	$ 0.3	$ 0.3