Condensed Consolidated Statements of Changes in Shareholders' Equity - USD ($) shares in Millions, $ in Millions	Total	Consolidated Funds	Ordinary shares Investments in unconsolidated Funds	Additional Paid-in Capital Investments in unconsolidated Funds	Retained earnings (deficit) Investments in unconsolidated Funds	Accumulated other comprehensive income (loss) Investments in unconsolidated Funds	Total shareholders’ equity Investments in unconsolidated Funds	Non- controlling interests Investments in unconsolidated Funds	Non- controlling interests Consolidated Funds
Beginning balance (in shares) at Dec. 31, 2017			109.7
Beginning balance at Dec. 31, 2017	$ 127.3		$ 0.1	$ 831.5	$ (734.6)	$ (21.6)	$ 75.4	$ 1.3	$ 50.6
Increase (Decrease) in Stockholders' Equity
Issuance of ordinary shares (in shares)			1.0
Repurchase of ordinary shares/common stock (in shares)			(4.4)
Repurchase of ordinary shares/common stock	(62.1)			(62.1)			(62.1)
Capital contributions	9.3	$ 68.0							9.3
Equity-based compensation	4.2			4.2			4.2
Foreign currency translation adjustment	(1.2)					(1.2)	(1.2)
Amortization related to derivative securities, net of tax	1.8					1.8	1.8
Other changes in non-controlling interests	0.1							0.1
Dividends	(31.6)				(31.6)		(31.6)
Dividends to related parties	0.0
Net income (loss)	111.6				113.4		113.4		(1.8)
Ending balance (in shares) at Sep. 30, 2018			106.3
Ending balance at Sep. 30, 2018	101.3		$ 0.1	773.6	(652.8)	(21.0)	99.9	1.4	0.0
Beginning balance at Dec. 31, 2017		44.0
Increase (Decrease) in redeemable non-controlling interest in consolidated Funds
Net de-consolidation of Funds	(58.1)	(41.5)							(58.1)
Net income (loss)		(0.1)
Ending balance at Sep. 30, 2018		70.4
Beginning balance at Dec. 31, 2017	171.3
Increase (Decrease) in total equity and redeemable non-controlling interest in consolidated Funds
Issuance of ordinary shares/common stock	0.0
Repurchase of common stock	(62.1)
Capital contributions	77.3
Equity-based compensation	4.2
Foreign currency translation adjustment	(1.2)
Amortization related to derivative securities, net of tax	1.8
Net de-consolidation of Funds	(99.6)
Dividends	(31.6)
Dividends to related parties	0.0
Net income (loss)	111.5
Ending balance at Sep. 30, 2018	171.7
Beginning balance (in shares) at Jun. 30, 2018			108.9
Beginning balance at Jun. 30, 2018	149.1		$ 0.1	806.9	(696.2)	(21.2)	89.6	1.4	58.1
Increase (Decrease) in Stockholders' Equity
Repurchase of ordinary shares/common stock (in shares)			(2.6)
Repurchase of ordinary shares/common stock	(34.7)			(34.7)			(34.7)
Capital contributions	0.1	64.2			0.1		0.1
Equity-based compensation	1.3			1.3			1.3
Foreign currency translation adjustment	(0.4)					(0.4)	(0.4)
Amortization related to derivative securities, net of tax	0.6					0.6	0.6
Dividends	(10.6)				(10.6)		(10.6)
Net income (loss)	54.0				54.0		54.0
Ending balance (in shares) at Sep. 30, 2018			106.3
Ending balance at Sep. 30, 2018	101.3		$ 0.1	773.6	(652.8)	(21.0)	99.9	1.4	0.0
Beginning balance at Jun. 30, 2018		6.0
Increase (Decrease) in redeemable non-controlling interest in consolidated Funds
Net de-consolidation of Funds	(58.1)								(58.1)
Net income (loss)		0.2
Ending balance at Sep. 30, 2018		70.4
Beginning balance at Jun. 30, 2018	155.1
Increase (Decrease) in total equity and redeemable non-controlling interest in consolidated Funds
Repurchase of common stock	(34.7)
Capital contributions	64.3
Equity-based compensation	1.3
Foreign currency translation adjustment	(0.4)
Amortization related to derivative securities, net of tax	0.6
Net de-consolidation of Funds	(58.1)
Dividends	(10.6)
Net income (loss)	54.2
Ending balance at Sep. 30, 2018	171.7
Beginning balance (in shares) at Dec. 31, 2018			105.2
Beginning balance at Dec. 31, 2018	134.2		$ 0.1	764.6	(640.5)	(20.9)	103.3	1.6	29.3
Increase (Decrease) in Stockholders' Equity
Issuance of ordinary shares (in shares)			0.2
Repurchase of ordinary shares/common stock (in shares)			(16.6)
Repurchase of ordinary shares/common stock	(209.3)			(209.3)			(209.3)
Capital contributions	4.9	36.3							4.9
Equity-based compensation	5.1			5.1			5.1
Foreign currency translation adjustment	(0.9)					(0.9)	(0.9)
Amortization related to derivative securities, net of tax	1.8					1.8	1.8
Other changes in non-controlling interests	0.3							0.3
Net de-consolidation of Funds	0.0
Dividends	(27.3)				(27.3)		(27.3)
Net income (loss)	162.0				156.1		156.1		5.9
Ending balance (in shares) at Sep. 30, 2019			88.8
Ending balance at Sep. 30, 2019	70.8		$ 0.1	560.4	(511.7)	(20.0)	28.8	1.9	40.1
Beginning balance at Dec. 31, 2018		41.9
Increase (Decrease) in redeemable non-controlling interest in consolidated Funds
Net income (loss)		3.7
Ending balance at Sep. 30, 2019		81.9
Beginning balance at Dec. 31, 2018	176.1
Increase (Decrease) in total equity and redeemable non-controlling interest in consolidated Funds
Issuance of ordinary shares/common stock	0.0
Repurchase of common stock	(209.3)
Capital contributions	41.2
Equity-based compensation	5.1
Foreign currency translation adjustment	(0.9)
Amortization related to derivative securities, net of tax	1.8
Net de-consolidation of Funds	0.0
Dividends	(27.3)
Net income (loss)	165.7
Ending balance at Sep. 30, 2019	152.7
Beginning balance (in shares) at Jun. 30, 2019			91.6
Beginning balance at Jun. 30, 2019	21.8		$ 0.1	585.2	(578.2)	(19.8)	(12.7)	1.8	32.7
Increase (Decrease) in Stockholders' Equity
Repurchase of ordinary shares/common stock (in shares)			(2.8)
Repurchase of ordinary shares/common stock	(25.5)			(25.5)			(25.5)
Capital contributions	0.9	(1.0)							0.9
Equity-based compensation	0.7			0.7			0.7
Foreign currency translation adjustment	(0.8)					(0.8)	(0.8)
Amortization related to derivative securities, net of tax	0.6					0.6	0.6
Amendment of Deferred Tax Asset Deed	0.0
Other changes in non-controlling interests	0.1							0.1
Dividends	(8.9)				(8.9)		(8.9)
Dividends to related parties	0.0
Net income (loss)	81.9				75.4		75.4		6.5
Ending balance (in shares) at Sep. 30, 2019			88.8
Ending balance at Sep. 30, 2019	70.8		$ 0.1	$ 560.4	$ (511.7)	$ (20.0)	$ 28.8	$ 1.9	$ 40.1
Beginning balance at Jun. 30, 2019		81.8
Increase (Decrease) in redeemable non-controlling interest in consolidated Funds
Net income (loss)		1.1
Ending balance at Sep. 30, 2019		$ 81.9
Beginning balance at Jun. 30, 2019	103.6
Increase (Decrease) in total equity and redeemable non-controlling interest in consolidated Funds
Repurchase of common stock	(25.5)
Capital contributions	(0.1)
Equity-based compensation	0.7
Foreign currency translation adjustment	(0.8)
Amortization related to derivative securities, net of tax	0.6
Dividends	(8.9)
Dividends to related parties	0.0
Net income (loss)	83.0
Ending balance at Sep. 30, 2019	$ 152.7