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Accumulated Other Comprehensive Income (Loss) - Changes in Accumulated Other Comprehensive Income (Loss) by Component (Details) - USD ($)
$ in Millions
 12 Months Ended
Sep. 30, 2025
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Balance at beginning of year $ (419.5) $ (509.3) $ (621.0)  
Other comprehensive income (loss) before reclassifications, net of tax (32.5) 89.4 108.1  
Reclassifications to compensation and benefits expense, net of tax 2.0 0.4 (0.7)  
Reclassifications to net investment and other income, net of tax 2.9   4.3  
Total other comprehensive income (loss) (27.6) 89.8 111.7  
Balance at end of year (447.1) (419.5) (509.3)  
Accumulated Other Comprehensive Income (Loss), Foreign Currency Translation Adjustment, Net of Tax (430.9) (412.5) (502.3) $ (615.1)
Accumulated Other Comprehensive (Income) Loss, Defined Benefit Plan, after Tax (16.8) (7.5) (7.6) (6.3)
AOCI, Debt Securities, Available-for-Sale, Adjustment, after Tax 0.6 0.5 0.6 $ 0.4
Currency Translation Adjustments [Member]        
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Other comprehensive income (loss) before reclassifications, net of tax (21.3) 89.8 108.5  
Reclassifications to compensation and benefits expense, net of tax 0.0 0.0 0.0  
Reclassifications to net investment and other income, net of tax 2.9   4.3  
Total other comprehensive income (loss) (18.4) 89.8 112.8  
Unrealized Losses on Defined Benefit Plans [Member]        
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Other comprehensive income (loss) before reclassifications, net of tax (11.3) (0.3) (0.6)  
Reclassifications to compensation and benefits expense, net of tax 2.0 0.4 (0.7)  
Reclassifications to net investment and other income, net of tax 0.0   0.0  
Total other comprehensive income (loss) (9.3) 0.1 (1.3)  
Unrealized Gains on Investments [Member]        
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Other comprehensive income (loss) before reclassifications, net of tax 0.1 (0.1) 0.2  
Reclassifications to compensation and benefits expense, net of tax 0.0 0.0 0.0  
Reclassifications to net investment and other income, net of tax 0.0   0.0  
Total other comprehensive income (loss) $ 0.1 $ (0.1) $ 0.2