Share Capital - Authorized and issued (Details)	12 Months Ended									0 Months Ended					12 Months Ended
	Dec. 31, 2014 USD ($)		Dec. 31, 2014 EUR (€)		Dec. 31, 2013 USD ($)		Dec. 31, 2014 Ordinary Shares USD ($)	Dec. 31, 2014 Undesignated shares USD ($)	Dec. 31, 2014 Subscriber shares EUR (€)	Oct. 15, 2011 Series D preference ordinary shares USD ($)	Oct. 15, 2011 Series D preference ordinary shares LIBOR	Mar. 15, 2007 Series E preference ordinary shares USD ($)	Dec. 31, 2013 February 2013 share repurchase plan USD ($)	Feb. 22, 2013 February 2013 share repurchase plan USD ($)	Dec. 31, 2014 Two Thousand Fourteen Share Repurchase Authorization [Member] USD ($)	Feb. 21, 2014 Two Thousand Fourteen Share Repurchase Authorization [Member] USD ($)
Shareholders Equity Disclosure [Line Items]
Authorized share capital, value	$ 9,999,900		€ 40,000
Ordinary shares, shares authorized (in shares)	999,990,000		999,990,000		999,990,000		500,000,000	499,990,000	40,000
Ordinary shares, par value (in dollars per share)	$ 0.01				$ 0.01		$ 0.01	$ 0.01	€ 1
Rollforward of ordinary shares issued and outstanding:
Balance at beginning of year, shares	278,253,308		278,253,308		298,682,000
Exercise of options, shares	424,000		424,000		927,000
Net issuance of restricted shares, shares	1,246,000		1,246,000		1,240,000
Share buybacks, shares	(24,740,000)	[1]	(24,740,000)	[1]	(22,596,000)	[1]
Balance at end of year, shares	255,182,955		255,182,955		278,253,308
Ordinary share buybacks:
Share repurchase authorization														850,000,000		1,000,000,000
Shares purchased and canceled during the period															24,700,000
Value of shares purchased and canceled during the period															800,000,000
Average price per share of shares repurchased and canceled during the period															$ 32.40
Amount remaining under share repurchase plan													275,000,000		267,600,000	200,000,000
Preferred shares and non-controlling interest in equity of consolidated subsidiaries:
Shares purchased and canceled during the period															24,700,000
Liquidation preference per share												$ 1,000.0
Preferred shares, shares issued												1,000,000
Preferred shares, stated dividend per share												$ 32.5
Dividend rate, spread on LIBOR											3.12%
Preferred shares, par value												$ 0.01
Proceeds on issuance of preferred shares										350,000,000		983,800,000
Face value of notes repaid										$ 600,000,000
Articles Of Association maximum voting power, percentage	10.00%		10.00%

[1] Includes share buybacks associated with authorized share buyback programs as well as purchases related to satisfying tax withholding obligations of employees in connection with the vesting of restricted shares granted under the Company’s equity compensation programs.