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Variable Interest Entities and Noncontrolling Interests - Other variable interest entity disclosures (Details) - USD ($)
$ in Thousands
Sep. 30, 2021
Dec. 31, 2020
Variable Interest Entity [Line Items]    
Total VIE Assets $ 44,783,736 $ 43,282,297
Maximum Exposure to Loss, Total 2,918,177 2,232,609
Variable Interest Entity, Not Primary Beneficiary    
Variable Interest Entity [Line Items]    
Total VIE Assets 4,731,717 3,859,058
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (4,710) (7,969)
Maximum Exposure to Loss - Off-Balance Sheet 52,461 56,320
Maximum Exposure to Loss, Total 47,751 48,351
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2017-1 Ltd. (Oct-17)    
Variable Interest Entity [Line Items]    
Total VIE Assets 145,573 145,573
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (214) (245)
Maximum Exposure to Loss - Off-Balance Sheet 585 844
Maximum Exposure to Loss, Total 371 599
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-1 Ltd. (Apr-18)    
Variable Interest Entity [Line Items]    
Total VIE Assets 228,938 250,095
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (764) (903)
Maximum Exposure to Loss - Off-Balance Sheet 1,683 2,245
Maximum Exposure to Loss, Total 919 1,342
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-2 Ltd. (Aug-18)    
Variable Interest Entity [Line Items]    
Total VIE Assets 0 108,395
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability 0 (138)
Maximum Exposure to Loss - Off-Balance Sheet 0 280
Maximum Exposure to Loss, Total 0 142
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-3 Ltd. (Oct-18)    
Variable Interest Entity [Line Items]    
Total VIE Assets 302,563 302,563
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (1,049) (1,320)
Maximum Exposure to Loss - Off-Balance Sheet 2,328 3,262
Maximum Exposure to Loss, Total 1,279 1,942
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-1 Ltd. (Mar-19)    
Variable Interest Entity [Line Items]    
Total VIE Assets 210,529 219,256
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (931) (1,361)
Maximum Exposure to Loss - Off-Balance Sheet 8,142 8,461
Maximum Exposure to Loss, Total 7,211 7,100
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-2 Ltd. (Apr-19)    
Variable Interest Entity [Line Items]    
Total VIE Assets 398,316 398,316
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (787) (730)
Maximum Exposure to Loss - Off-Balance Sheet 5,658 5,201
Maximum Exposure to Loss, Total 4,871 4,471
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-3 Ltd. (Jul-19)    
Variable Interest Entity [Line Items]    
Total VIE Assets 491,634 528,084
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (826) (861)
Maximum Exposure to Loss - Off-Balance Sheet 3,971 5,079
Maximum Exposure to Loss, Total 3,145 4,218
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-4 Ltd. (Oct-19)    
Variable Interest Entity [Line Items]    
Total VIE Assets 468,737 468,737
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (682) (890)
Maximum Exposure to Loss - Off-Balance Sheet 4,761 6,676
Maximum Exposure to Loss, Total 4,079 5,786
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-1 Ltd. (Jun-20)    
Variable Interest Entity [Line Items]    
Total VIE Assets [1] 0 275,068
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability [1] 0 (178)
Maximum Exposure to Loss - Off-Balance Sheet [1] 0 1,012
Maximum Exposure to Loss, Total [1] 0 834
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-1 Ltd. (Jun-20) | Funded by directly provided capacity    
Variable Interest Entity [Line Items]    
Initial Coverage, Amount 79,000  
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-2 Ltd (Sep-20)    
Variable Interest Entity [Line Items]    
Total VIE Assets [2] 266,704 423,420
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability [2] (279) (556)
Maximum Exposure to Loss - Off-Balance Sheet [2] 2,629 6,839
Maximum Exposure to Loss, Total [2] 2,350 6,283
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-2 Ltd (Sep-20) | Funded by directly provided capacity    
Variable Interest Entity [Line Items]    
Initial Coverage, Amount 26,000  
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-3 Ltd. (Nov-20)    
Variable Interest Entity [Line Items]    
Total VIE Assets [3] 381,410 418,158
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability [3] (395) (631)
Maximum Exposure to Loss - Off-Balance Sheet [3] 6,646 9,605
Maximum Exposure to Loss, Total [3] 6,251 8,974
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-3 Ltd. (Nov-20) | Funded by directly provided capacity    
Variable Interest Entity [Line Items]    
Initial Coverage, Amount 34,000  
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-4 Ltd. (Dec-20)    
Variable Interest Entity [Line Items]    
Total VIE Assets [4] 226,916 321,393
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability [4] (100) (156)
Maximum Exposure to Loss - Off-Balance Sheet [4] 2,190 6,816
Maximum Exposure to Loss, Total [4] 2,090 6,660
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-4 Ltd. (Dec-20) | Funded by directly provided capacity    
Variable Interest Entity [Line Items]    
Initial Coverage, Amount 16,000  
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-1 Ltd. (Mar-21)    
Variable Interest Entity [Line Items]    
Total VIE Assets 579,717 [5] 0
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability 229 [5] 0
Maximum Exposure to Loss - Off-Balance Sheet 4,217 [5] 0
Maximum Exposure to Loss, Total 4,446 [5] 0
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-1 Ltd. (Mar-21) | Funded by directly provided capacity    
Variable Interest Entity [Line Items]    
Initial Coverage, Amount 64,000  
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-2 Ltd. (Jun-21)    
Variable Interest Entity [Line Items]    
Total VIE Assets 522,807 [6] 0
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability 906 [6] 0
Maximum Exposure to Loss - Off-Balance Sheet 5,090 [6] 0
Maximum Exposure to Loss, Total 5,996 [6] 0
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-2 Ltd. (Jun-21) | Funded by directly provided capacity    
Variable Interest Entity [Line Items]    
Initial Coverage, Amount 93,000  
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-3 Ltd. (Sep-21)    
Variable Interest Entity [Line Items]    
Total VIE Assets 507,873 [7] 0
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability 182 [7] 0
Maximum Exposure to Loss - Off-Balance Sheet 4,561 [7] 0
Maximum Exposure to Loss, Total 4,743 [7] $ 0
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-3 Ltd. (Sep-21) | Funded by directly provided capacity    
Variable Interest Entity [Line Items]    
Initial Coverage, Amount $ 131,000  
[1]  An additional $79 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table
[2] An additional $26 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.
[3] An additional $34 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.
[4] An additional $16 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.
[5] An additional $64 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table
[6]  An additional $93 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.
[7] An additional $131 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table