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Contracts Accounted for as Insurance - Narrative (Details)
9 Months Ended 12 Months Ended
Sep. 30, 2018
Sep. 30, 2017
Dec. 31, 2017
Guarantor Obligations [Line Items]      
Weighted average risk-free rates for U.S. dollar denominated financial guaranty insurance obligations 3.04%   2.39%
Minimum [Member]      
Guarantor Obligations [Line Items]      
Weighted average risk-free rates for U.S. dollar denominated financial guaranty insurance obligations 0.00%   0.00%
Maximum [Member]      
Guarantor Obligations [Line Items]      
Weighted average risk-free rates for U.S. dollar denominated financial guaranty insurance obligations 3.20%   2.78%
Foreign Currency Concentration Risk [Member] | Premiums Receivable [Member]      
Guarantor Obligations [Line Items]      
Percentage of installment premiums denominated in currencies other than the U.S. dollar 72.00% 71.00% 72.00%