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Revenues - Schedule of Operating Revenues by Geographic Area (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
Jun. 30, 2023
Jun. 30, 2022
Jun. 30, 2023
Jun. 30, 2022
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area $ 1,969.0 $ 2,031.3 $ 5,863.3 $ 6,336.3
Investment management fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 1,613.4 1,636.1 4,818.5 5,045.8
Sales and distribution fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 304.0 335.6 897.3 1,104.0
Shareholder servicing fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 38.8 46.9 115.5 146.8
Other [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 12.8 12.7 32.0 39.7
United States [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 1,488.0 1,522.3 4,427.3 4,653.5
United States [Member] | Investment management fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 1,232.3 1,234.7 3,672.9 3,720.8
United States [Member] | Sales and distribution fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 213.5 238.1 634.1 778.1
United States [Member] | Shareholder servicing fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 30.3 37.5 90.2 116.4
United States [Member] | Other [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 11.9 12.0 30.1 38.2
Luxembourg [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 276.2 300.6 812.4 1,004.2
Luxembourg [Member] | Investment management fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 192.3 211.6 570.7 707.2
Luxembourg [Member] | Sales and distribution fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 75.4 80.2 217.4 268.3
Luxembourg [Member] | Shareholder servicing fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 8.0 8.5 23.5 27.9
Luxembourg [Member] | Other [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 0.5 0.3 0.8 0.8
Asia-Pacific [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 70.3 77.6 231.9 264.1
Asia-Pacific [Member] | Investment management fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 64.3 71.2 214.4 242.5
Asia-Pacific [Member] | Sales and distribution fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 5.1 5.8 15.1 20.0
Asia-Pacific [Member] | Shareholder servicing fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 0.5 0.4 1.6 1.1
Asia-Pacific [Member] | Other [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 0.4 0.2 0.8 0.5
Americas Excluding United States [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 63.9 71.0 192.9 232.1
Americas Excluding United States [Member] | Investment management fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 53.9 59.4 162.0 194.3
Americas Excluding United States [Member] | Sales and distribution fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 10.0 11.5 30.7 37.6
Americas Excluding United States [Member] | Shareholder servicing fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 0.0 0.1 0.2 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 70.6 59.8 198.8 182.4
Europe, Middle East and Africa, Excluding Luxembourg [Member] | Investment management fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 70.6 59.2 198.5 181.0
Europe, Middle East and Africa, Excluding Luxembourg [Member] | Sales and distribution fees [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area 0.0 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 0.4 0.0 1.2
Europe, Middle East and Africa, Excluding Luxembourg [Member] | Other [Member]        
Disaggregation of Revenue [Line Items]        
Operating revenues by geographic area $ 0.0 $ 0.2 $ 0.3 $ 0.2