Income Taxes - Valuation Allowance (Detail) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Valuation Allowance [Line Items]
Valuation allowance	$ 92.3	$ 97.4
Change in valuation allowance	2.4	29.2	$ (63.6)
Income tax expense (benefit)	38.6	(20.5)	$ 29.3
U.S. losses and other federal deferred tax benefits
Valuation Allowance [Line Items]
Valuation allowance	42.9	46.5
Net operating losses in Luxembourg subsidiaries
Valuation Allowance [Line Items]
Valuation allowance	25.2
Net Operating Losses in Israel Subsidiaries
Valuation Allowance [Line Items]
Valuation allowance	21.9	20.0
Net Operating Losses in United Kingdom Subsidiaries
Valuation Allowance [Line Items]
Valuation allowance	2.3
Luxembourg | U.S. losses and other federal deferred tax benefits
Valuation Allowance [Line Items]
Change in valuation allowance	(1.6)	4.2
United Kingdom | Net Operating Losses in United Kingdom Subsidiaries
Valuation Allowance [Line Items]
Change in valuation allowance	(1.9)	1.0
United States | Net Operating Losses in US Branches
Valuation Allowance [Line Items]
Income tax expense (benefit)	0.6
Israel | Net Operating Losses in Israel Subsidiaries
Valuation Allowance [Line Items]
Change in valuation allowance	1.9	2.7
Subsidiaries | Luxembourg | Net operating losses in Luxembourg subsidiaries
Valuation Allowance [Line Items]
Valuation allowance		26.8
Subsidiaries | United Kingdom | Net operating losses in Luxembourg subsidiaries
Valuation Allowance [Line Items]
Valuation allowance		4.1
Guilford Holdings, Inc. | United States
Valuation Allowance [Line Items]
Change in valuation allowance	(3.6)
Income tax expense (benefit)		14.9
BAM | United States
Valuation Allowance [Line Items]
Income tax expense (benefit)	7.8	4.5
BAM | United States | MSC
Valuation Allowance [Line Items]
Income tax expense (benefit)	(7.5)	(9.7)
BAM | United States | Foreign Tax Credits
Valuation Allowance [Line Items]
Income tax expense (benefit)	$ (0.8)	$ 1.9