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Significant Transactions (Acquisitions) (Details)
 3 Months Ended 8 Months Ended 12 Months Ended
Jun. 28, 2019
USD ($)
Apr. 04, 2019
USD ($)
Apr. 01, 2019
USD ($)
Dec. 03, 2018
USD ($)
May 11, 2018
USD ($)
Jan. 24, 2018
USD ($)
Dec. 31, 2019
USD ($)
Mar. 31, 2019
USD ($)
Sep. 30, 2018
USD ($)
Jun. 30, 2018
USD ($)
Dec. 31, 2018
USD ($)
Dec. 31, 2019
USD ($)
earnout_period
Dec. 31, 2018
USD ($)
Dec. 31, 2017
USD ($)
May 31, 2019
USD ($)
Apr. 03, 2019
Feb. 26, 2019
May 18, 2018
USD ($)
Feb. 05, 2018
USD ($)
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Other Investments             $ 622,800,000       $ 165,700,000 $ 622,800,000 $ 165,700,000            
Equity method investment, aggregate cost                                     $ 125,000,000.0
Purchases of consolidated subsidiaries, net of cash acquired                       258,000,000.0 295,200,000 $ 27,600,000          
Change in fair value of contingent consideration earnout liabilities                       2,100,000 2,700,000            
Payments to acquire business, net   $ 81,400,000                                  
Goodwill             394,700,000       379,900,000 394,700,000 379,900,000            
NSM Holding Co LLC                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Long-term line of credit         $ 100,000,000.0                            
Change in fair value of contingent consideration earnout liabilities                     2,700,000 2,100,000              
Contingent consideration earnout liabilities             20,600,000       20,200,000 20,600,000 20,200,000            
White Mountains                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Other Investments             $ 856,300,000       $ 325,600,000 $ 856,300,000 $ 325,600,000            
MediaAlpha                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Ownership interest (as a percent)                                 48.30%    
Fully diluted ownership interest (as a percent)                                 42.00%    
Elementum Holdings, L.P.                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Ownership interest (as a percent)             30.00%         30.00%     30.00%        
Other Investments                             $ 55,100,000        
Insurance-Linked Securities Funds                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Commitment                             $ 50,000,000.0        
Elementum Funds                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Equity method investment, aggregate cost             $ 40,000,000.0         $ 40,000,000.0              
NSM Insurance HoldCo, LLC                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Ownership interest (as a percent)         95.00%   96.40%       95.50% 96.40% 95.50%            
Purchases of consolidated subsidiaries, net of cash acquired         $ 274,200,000                            
Purchase price adjustment                 $ 2,100,000                    
Assets acquired         495,200,000                            
Goodwill and intangible assets acquired         383,000,000.0                            
Liabilities acquired         204,600,000                            
Contingent consideration         10,200,000                            
Noncontrolling interest acquired         $ 14,400,000                            
Transaction costs                   $ 6,300,000                  
Number of earnout periods | earnout_period                       2              
Fully diluted ownership interest (as a percent)         83.60%   88.40%       85.00% 88.40% 85.00%            
Fresh Insurance Services Group Limited                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Ownership interest (as a percent)                                   100.00%  
Equity method investment, aggregate cost                                   $ 49,600,000  
Purchase price adjustment               $ 700,000                      
Assets acquired                                   72,600,000  
Goodwill and intangible assets acquired                                   54,600,000  
Liabilities acquired                                   22,300,000  
Contingent consideration                                   7,500,000  
KBK Insurance Group, Inc. & KBK Premium Services, Inc.                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Purchases of consolidated subsidiaries, net of cash acquired       $ 60,000,000.0                              
Goodwill and intangible assets acquired       59,400,000     $ 32,600,000         $ 32,600,000              
Stock issued during period, value, acquisitions       29,000,000.0                              
Proceeds from borrowings       $ 30,100,000                              
Intangible assets acquired             $ 32,700,000         $ 32,700,000              
Change in fair value of contingent consideration earnout liabilities               $ 5,900,000                      
AIG Collector Car Business                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Purchases of consolidated subsidiaries, net of cash acquired $ 82,500,000                                    
Intangible assets acquired 82,500,000                                    
AIG Collector Car Business | NSM Holding Co LLC                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Proceeds from borrowings 22,500,000                                    
AIG Collector Car Business | White Mountains                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Stock issued during period, value, acquisitions $ 59,100,000                                    
DavidShield                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Ownership interest (as a percent)           50.00%                          
PassportCard                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Ownership interest (as a percent)           50.00%                          
DavidShield & PassportCard                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Ownership interest (as a percent)             50.00%       50.00% 50.00% 50.00%            
Payments to acquire businesses, gross           $ 41,800,000                          
Payments to acquire business, net           $ 28,300,000                          
Kudu                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Ownership interest (as a percent)   99.10%                           49.50%     49.50%
Assets acquired   $ 155,500,000                                 $ 155,500,000
Liabilities acquired   800,000                                 800,000
Noncontrolling interest acquired   1,500,000                                 1,500,000
Goodwill   7,600,000                                 7,600,000
Intangible assets acquired   $ 2,200,000                                 $ 2,200,000
Fully diluted ownership interest (as a percent)   85.40%                           42.70%     42.70%
Funded capital commitment   $ 250,000,000.0         $ 350,000,000.0         $ 350,000,000.0              
Increase in capital commitment             100,000,000.0                        
Unfunded capital commitment             129,000,000.0         129,000,000.0              
NSM Bank Facility | NSM Holding Co LLC                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Total commitment under revolving credit facility         $ 234,000,000.0                            
NSM Bank Facility | Term Loan | NSM Holding Co LLC                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Long-term line of credit             221,300,000       $ 180,400,000 221,300,000 $ 180,400,000         $ 51,000,000.0  
Proceeds from borrowings                       42,900,000              
Total commitment under revolving credit facility         $ 224,000,000.0                            
Kudu Debt | Delayed Draw Term Loans | Kudu                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Total commitment under revolving credit facility             125,000,000.0         125,000,000.0              
Undrawn amount on facility             $ 68,000,000.0         68,000,000.0              
Embrace Pet Insurance                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Goodwill and intangible assets acquired     $ 67,600,000                                
Intangible assets acquired     15,400,000                                
Goodwill     52,200,000                                
Embrace Pet Insurance | NSM Holding Co LLC                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Stock issued during period, value, acquisitions     58,200,000                                
Proceeds from borrowings     $ 20,400,000                                
Percentage of voting interests acquired     100.00%                                
Payments to acquire businesses, gross     $ 71,500,000                                
Embrace Pet Insurance | NSM Bank Facility | Term Loan | NSM Holding Co LLC                                      
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]                                      
Proceeds from borrowings                       $ 20,400,000