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Segment Information (Details) - USD ($)
$ in Millions
 3 Months Ended 9 Months Ended
Sep. 30, 2018
Sep. 30, 2017
Sep. 30, 2018
Sep. 30, 2017
Segment reporting information        
Earned insurance premiums $ 3.3 $ 2.4 $ 9.7 $ 6.6
Net investment income 13.4 12.2 44.9 39.7
Net realized and unrealized investment (losses) gains 66.1 32.5 22.9 102.5
Commission revenues 112.2   278.6 103.9
Other revenue 3.7 1.6 7.0 7.1
Total revenues 198.7 87.5 363.1 259.8
Insurance acquisition expenses 1.2 0.9 3.9 3.0
Other underwriting expenses 0.1 0.1 0.3 0.3
Cost of sales 62.9   182.0 88.7
General and administrative and other expenses 68.5 41.7 174.6 156.1
Broker commission expense 10.9   17.5  
Amortization 7.4 2.4 12.9 7.3
Interest expense 3.4 0.9 6.0 1.8
Total expenses 154.4 79.1 397.2 257.2
Pre-tax income (loss) $ 44.3 $ 8.4 $ (34.1) $ 2.6
MediaAlpha        
Segment reporting information        
Percentage of advertising revenue 30.00% 32.00% 31.00% 29.00%
HG Global-BAM | HG Global-BAM        
Segment reporting information        
Earned insurance premiums $ 3.3 $ 2.4 $ 9.7 $ 6.6
Net investment income 4.8 3.3 12.5 8.9
Net realized and unrealized investment (losses) gains (4.1) 0.8 (14.4) 3.2
Commission revenues 0.0   0.0 0.0
Other revenue 0.2 0.2 0.8 0.8
Total revenues 4.2 6.7 8.6 19.5
Insurance acquisition expenses 1.2 0.9 3.9 3.0
Other underwriting expenses 0.1 0.1 0.3 0.3
Cost of sales 0.0     0.0
General and administrative and other expenses 11.3 10.6 36.5 31.5
Broker commission expense 0.0   0.0  
Amortization 0.0 0.0 0.0  
Interest expense 0.0 0.0   0.0
Total expenses 12.6 11.6 40.7 34.8
Pre-tax income (loss) (8.4) (4.9) (32.1) (15.3)
NSM Holding Co LLC | NSM Holding Co LLC        
Segment reporting information        
Earned insurance premiums 0.0   0.0  
Net investment income 0.0   0.0  
Net realized and unrealized investment (losses) gains 0.0   0.0  
Commission revenues 36.6   59.2 0.0
Other revenue 3.1 0.0 4.0 0.0
Total revenues 39.7 0.0 63.2 0.0
Insurance acquisition expenses 0.0   0.0  
Other underwriting expenses 0.0   0.0  
Cost of sales 0.0   0.0  
General and administrative and other expenses 25.8 0.0 37.9 0.0
Broker commission expense 10.9 0.0 17.5 0.0
Amortization 5.0 0.0 5.0 0.0
Interest expense 3.2 0.0 4.8 0.0
Total expenses 44.9 0.0 65.2 0.0
Pre-tax income (loss) (5.2)   (2.0)  
MediaAlpha | MediaAlpha        
Segment reporting information        
Earned insurance premiums 0.0 0.0   0.0
Net investment income 0.0 0.0   0.0
Net realized and unrealized investment (losses) gains 0.0 0.0   0.0
Commission revenues 74.5 37.9 216.4 101.2
Other revenue 0.0   1.6 0.0
Total revenues 74.5 37.9 218.0 101.2
Insurance acquisition expenses 0.0 0.0   0.0
Other underwriting expenses 0.0 0.0   0.0
Cost of sales 61.8 32.2 179.1 86.0
General and administrative and other expenses 5.4 3.8 21.2 10.7
Broker commission expense 0.0   0.0  
Amortization 2.4 2.3 7.8 7.2
Interest expense 0.2 0.1 0.9 0.6
Total expenses 69.8 38.4 209.0 104.5
Pre-tax income (loss) 4.7 (0.5) 9.0 (3.3)
Other | Other Segment        
Segment reporting information        
Earned insurance premiums 0.0 0.0 0.0 0.0
Net investment income 8.6 8.9 32.4 30.8
Net realized and unrealized investment (losses) gains 70.2 31.7 37.3 99.3
Commission revenues 1.1 0.9 3.0 2.7
Other revenue 0.4 1.4 0.6 6.3
Total revenues 80.3 42.9 73.3 139.1
Insurance acquisition expenses 0.0 0.0 0.0 0.0
Other underwriting expenses 0.0 0.0 0.0 0.0
Cost of sales 1.1 0.9 2.9 2.7
General and administrative and other expenses 26.0 27.3 79.0 113.9
Broker commission expense 0.0   0.0  
Amortization 0.0 0.1 0.1 0.1
Interest expense 0.0 0.8 0.3 1.2
Total expenses 27.1 29.1 82.3 117.9
Pre-tax income (loss) $ 53.2 13.8 $ (9.0) $ 21.2
Advertising and Commission Revenue        
Segment reporting information        
Commission revenues   38.8    
Advertising and Commission Revenue | HG Global-BAM | HG Global-BAM        
Segment reporting information        
Commission revenues   0.0    
Service        
Segment reporting information        
Cost of sales   33.1    
Service | HG Global-BAM | HG Global-BAM        
Segment reporting information        
Cost of sales   $ 0.0