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Segment Reporting - Summary of Gross and Net Written and Earned Premiums, Underwriting Results, Ratios and Reserves for Each of Company's Business Segments (Details) - USD ($)
$ in Millions
 3 Months Ended 12 Months Ended
Dec. 31, 2017
Sep. 30, 2017
Jun. 30, 2017
Mar. 31, 2017
Dec. 31, 2016
Sep. 30, 2016
Jun. 30, 2016
Mar. 31, 2016
Dec. 31, 2015
Sep. 30, 2015
Jun. 30, 2015
Mar. 31, 2015
Dec. 31, 2017
Dec. 31, 2016
Dec. 31, 2015
Dec. 31, 2014
Segment Reporting Information [Line Items]                                
Gross written premiums                         $ 3,360.9 $ 3,147.0 $ 2,997.3  
Net written premiums                         2,212.5 2,593.7 2,646.2  
Gross earned premiums                         3,209.2 3,086.3 2,856.8  
Net earned premium $ 511.0 $ 652.5 $ 562.0 $ 581.1 $ 612.4 $ 681.0 $ 680.8 $ 663.1 $ 629.7 $ 640.6 $ 609.4 $ 593.6 2,306.6 2,637.3 2,473.3  
Losses and loss adjustment expenses 544.2 776.2 346.1 328.2 387.3 389.2 442.2 357.4 334.0 365.6 360.5 306.1 1,994.7 1,576.1 1,366.2  
Amortization of deferred policy acquisition costs 85.1 105.4 96.3 113.7 141.1 130.9 126.7 130.2 118.2 132.0 114.1 119.3 400.5 528.9 483.6  
General and administrative expenses                         411.2 406.6 360.1  
Underwriting income (loss)                         (499.8) 125.7 263.4  
Corporate expenses                         (58.3) (73.8) (63.9)  
Non-operating expenses                         (32.7) (9.7)    
Net investment income 47.5 46.4 47.4 47.7 43.2 46.4 48.0 49.5 46.4 45.0 46.7 47.4 189.0 187.1 185.5  
Realized and unrealized investment gains 18.8 29.9 49.0 51.2 (29.0) 26.7 45.1 65.6 12.9 10.7 13.5 57.4 148.9 108.4 94.5  
Realized and unrealized investment losses (4.0) (12.4) (7.0) (5.0) (29.1) (5.2) (8.3) (20.6) 17.7 (51.9) (28.8) (14.5) (28.4) (63.2) (77.5)  
Change in fair value of loan notes issued by variable interest entities 17.6 9.8 (3.3) (2.9) (3.4) (9.8) 0.5 (4.4) (5.3) (8.3) (3.3) (2.9) 21.2 (17.1) (19.8)  
Change in fair value of derivatives 2.5 4.5 17.6 3.1 (17.6) 0.6 (0.4) (7.2) 2.5 10.1 2.0 (7.8) 27.7 (24.6) 6.8  
Interest expense on long term debt (7.3) (7.4) (7.4) (7.4) (7.4) (7.3) (7.4) (7.4) (7.4) (7.4) (7.3) (7.4) (29.5) (29.5) (29.5)  
Net realized and unrealized foreign exchange (losses) (2.8) 8.4 (20.6) (8.9) 12.0 10.8 (5.3) (15.7) 5.0 (8.4) (11.6) (6.4) (23.9) 1.8 (21.4)  
Other income 3.9 (2.2) 3.6 3.6 3.3 1.5 (0.5) 1.4 (0.3) (2.3) (1.2) 3.9 8.9 5.7 0.1  
Other expenses                         (4.9) (1.3) (0.7)  
(Loss)/income from operations before income tax (195.1) (263.0) 77.0 99.3 (74.1) 100.5 66.2 116.9 123.2 30.0 51.2 133.1 (281.8) 209.5 337.5  
Income tax credit/(expense) 10.2 9.2 (1.2) (2.8) 2.6 (4.9) (1.3) (2.5) (5.3) (1.8) (2.2) (5.1) 15.4 (6.1) (14.4)  
Net (loss)/income (184.9) $ (253.8) $ 75.8 $ 96.5 (71.5) $ 95.6 $ 64.9 $ 114.4 117.9 $ 28.2 $ 49.0 $ 128.0 (266.4) 203.4 323.1  
Losses and loss adjustment expenses 6,749.5       5,319.9       4,938.2       6,749.5 5,319.9 4,938.2 $ 4,750.8
Net Reserves for Losses and LAE 5,234.3       4,759.2       4,583.4       $ 5,234.3 $ 4,759.2 $ 4,583.4 $ 4,400.8
Ratios                                
Loss ratio                         86.50% 59.80% 55.20%  
Policy acquisition expense ratio                         17.40% 20.10% 19.60%  
General and administrative expense ratio                         21.80% 18.60% 17.10%  
Expense ratio                         39.20% 38.70% 36.70%  
Combined ratio                         125.70% 98.50% 91.90%  
Reinsurance                                
Segment Reporting Information [Line Items]                                
Net written premiums                         $ 1,250.0 $ 1,269.2 $ 1,153.5  
Net earned premium                         1,206.1 1,181.9 1,072.6  
Losses and loss adjustment expenses 2,917.1       2,462.1       2,409.5       2,917.1 2,462.1 2,409.5  
Net Reserves for Losses and LAE 2,917.1       2,462.1       2,409.5       $ 2,917.1 $ 2,462.1 $ 2,409.5  
Ratios                                
Loss ratio                         92.60% 55.70% 45.80%  
Policy acquisition expense ratio                         19.50% 19.20% 20.90%  
General and administrative expense ratio                         13.00% 15.10% 13.70%  
Expense ratio                         32.50% 34.30% 34.60%  
Combined ratio                         125.10% 90.00% 80.40%  
Insurance                                
Segment Reporting Information [Line Items]                                
Net written premiums                         $ 962.5 $ 1,324.5 $ 1,492.7  
Net earned premium                         1,100.5 1,455.4 1,400.7  
Losses and loss adjustment expenses 2,317.2       2,297.1       2,173.9       2,317.2 2,297.1 2,173.9  
Net Reserves for Losses and LAE $ 2,317.2       $ 2,297.1       $ 2,173.9       $ 2,317.2 $ 2,297.1 $ 2,173.9  
Ratios                                
Loss ratio                         79.80% 63.10% 62.40%  
Policy acquisition expense ratio                         15.00% 20.80% 18.50%  
General and administrative expense ratio                         23.10% 15.70% 15.20%  
Expense ratio                         38.10% 36.50% 33.70%  
Combined ratio                         117.90% 99.60% 96.10%  
Operating Segments | Reinsurance                                
Segment Reporting Information [Line Items]                                
Gross written premiums                         $ 1,548.5 $ 1,413.2 $ 1,248.9  
Net written premiums                         1,250.0 1,269.2 1,153.5  
Gross earned premiums                         1,451.8 1,317.9 1,153.5  
Net earned premium                         1,206.1 1,181.9 1,072.6  
Losses and loss adjustment expenses                         1,116.4 657.9 491.6  
Amortization of deferred policy acquisition costs                         235.5 226.4 224.7  
General and administrative expenses                         157.3 178.2 146.5  
Underwriting income (loss)                         (303.1) 119.4 209.8  
Operating Segments | Insurance                                
Segment Reporting Information [Line Items]                                
Gross written premiums                         1,812.4 1,733.8 1,748.4  
Net written premiums                         962.5 1,324.5 1,492.7  
Gross earned premiums                         1,757.4 1,768.4 1,703.3  
Net earned premium                         1,100.5 1,455.4 1,400.7  
Losses and loss adjustment expenses                         878.3 918.2 874.6  
Amortization of deferred policy acquisition costs                         165.0 302.5 258.9  
General and administrative expenses                         253.9 228.4 213.6  
Underwriting income (loss)                         $ (196.7) $ 6.3 $ 53.6