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Variable Interest Entities and Noncontrolling Interests - Other variable interest entity disclosures (Details) - USD ($)
$ in Thousands
Sep. 30, 2020
Dec. 31, 2019
Variable Interest Entity [Line Items]    
Total VIE Assets $ 42,716,035 $ 37,885,361
Maximum Exposure to Loss 2,064,111 1,848,679
Variable Interest Entity, Not Primary Beneficiary    
Variable Interest Entity [Line Items]    
Total VIE Assets 3,329,940 3,425,833
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (10,471) (5,197)
Maximum Exposure to Loss - Off-Balance Sheet 74,743 42,084
Maximum Exposure to Loss 64,272 36,887
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2017-1 Ltd. (Oct-17)    
Variable Interest Entity [Line Items]    
Total VIE Assets 145,573 216,429
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (432) (442)
Maximum Exposure to Loss - Off-Balance Sheet 2,104 2,794
Maximum Exposure to Loss 1,672 2,352
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-1 Ltd. (Apr-18)    
Variable Interest Entity [Line Items]    
Total VIE Assets 250,095 328,482
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (1,592) (1,574)
Maximum Exposure to Loss - Off-Balance Sheet 4,821 5,757
Maximum Exposure to Loss 3,229 4,183
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-2 Ltd. (Aug-18)    
Variable Interest Entity [Line Items]    
Total VIE Assets 187,362 437,009
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (641) (877)
Maximum Exposure to Loss - Off-Balance Sheet 1,695 2,524
Maximum Exposure to Loss 1,054 1,647
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-3 Ltd. (Oct-18)    
Variable Interest Entity [Line Items]    
Total VIE Assets 302,563 426,806
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (2,477) (1,113)
Maximum Exposure to Loss - Off-Balance Sheet 7,261 3,937
Maximum Exposure to Loss 4,784 2,824
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-1 Ltd. (Mar-19)    
Variable Interest Entity [Line Items]    
Total VIE Assets 219,256 257,358
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (1,062) (226)
Maximum Exposure to Loss - Off-Balance Sheet 8,944 3,027
Maximum Exposure to Loss 7,882 2,801
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-2 Ltd. (Apr-19)    
Variable Interest Entity [Line Items]    
Total VIE Assets 398,316 525,959
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (1,090) (78)
Maximum Exposure to Loss - Off-Balance Sheet 11,369 2,579
Maximum Exposure to Loss 10,279 2,501
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-3 Ltd. (Jul-19)    
Variable Interest Entity [Line Items]    
Total VIE Assets 528,084 656,523
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (975) (585)
Maximum Exposure to Loss - Off-Balance Sheet 9,156 9,273
Maximum Exposure to Loss 8,181 8,688
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-4 Ltd. (Oct-19)    
Variable Interest Entity [Line Items]    
Total VIE Assets 468,737 577,267
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (1,179) (302)
Maximum Exposure to Loss - Off-Balance Sheet 12,722 12,193
Maximum Exposure to Loss 11,543 $ 11,891
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-1 Ltd. (Jun-20)    
Variable Interest Entity [Line Items]    
Total VIE Assets [1] 406,534  
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (701)  
Maximum Exposure to Loss - Off-Balance Sheet 7,590  
Maximum Exposure to Loss 6,889  
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] 423,420  
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability (322)  
Maximum Exposure to Loss - Off-Balance Sheet 9,081  
Maximum Exposure to Loss 8,759  
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  
[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.