Transactions with related parties - Transactions with ACGL (Details) $ in Thousands			3 Months Ended
		Aug. 01, 2019 USD ($)	Mar. 31, 2020 USD ($)	Mar. 31, 2019 USD ($)	Dec. 31, 2019 USD ($)	Jul. 02, 2019 USD ($)	Dec. 31, 2018 USD ($)	Mar. 31, 2014 USD ($) executive
Related Party Transaction [Line Items]
Repurchase of preference shares			$ 2,867	$ 0
Ceding fee expense			4,000	4,200
Consolidated statement of income (loss) items:
Gross premiums written			234,902	186,689
Gross premiums ceded			(48,202)	(41,302)
Net premiums earned			(140,039)	(146,094)
Loss and loss adjustment expenses			(110,676)	(110,850)
Acquisition expenses			(28,367)	(33,974)
Interest expense			2,912	0
Preference dividends			1,171	4,907
Consolidated balance sheet items:
Total investments			2,512,806		$ 2,709,137
Premiums receivable			281,541		273,657
Prepaid reinsurance premiums			128,570		132,577
Deferred acquisition costs, net			71,402		64,044
Funds held by reinsurers			40,520		42,505
Reserve for losses and loss adjustment expenses			1,300,249	1,104,532	1,263,628		$ 1,032,760
Unearned premiums			478,663		438,907
Losses payable			46,424		61,314
Reinsurance balances payable			71,204		77,066
Senior notes			172,486		172,418
Amounts due to affiliates			4,168		4,467
Contingently redeemable preference shares			$ 52,328	221,083	52,305		$ 220,992
ACGL and Subsidiaries | Arch Capital Group Limited
Related Party Transaction [Line Items]
Amount of investment by related party								$ 100,000
Percentage of common equity owned by related party			12.60%					11.00%
Related party - number of executives serving as directors | executive								2
Percentage of preference equity owned by related party			6.60%
Face amount of senior notes						$ 35,000
Consolidated statement of income (loss) items:
Interest expense			$ 582	0
Preference dividends			78	325
Consolidated balance sheet items:
Total investments			680,448		815,528
Premiums receivable			122,147		106,462
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses			88,179		79,597
Prepaid reinsurance premiums			74,696		75,249
Deferred acquisition costs, net			34,760		31,609
Funds held by reinsurers			26,964		29,867
Reserve for losses and loss adjustment expenses			684,802		693,861
Unearned premiums			160,328		143,852
Losses payable			32,146		39,619
Reinsurance balances payable			58,604		62,301
Senior notes			34,497		34,484	35,000
Amounts due to affiliates			32,146		4,467
Other liabilities - contingent commissions			3,911		5,516
Contingently redeemable preference shares			3,463		$ 3,462
ACGL and Subsidiaries | AUL and AUI
Consolidated statement of income (loss) items:
Acquisition expenses			(6,563)	(4,948)
Quota share business | ACGL and Subsidiaries | Arch Capital Group Limited
Consolidated statement of income (loss) items:
Gross premiums ceded			(19,828)	(16,990)
Net premiums earned			(19,788)	(12,940)
Loss and loss adjustment expenses			(15,815)	(9,138)
Acquisition expenses	[1]		(4,537)	(3,104)
Direct business | ACGL and Subsidiaries | Arch Capital Group Limited
Consolidated statement of income (loss) items:
Gross premiums written			81,348	72,005
Net premiums earned			(58,785)	(61,838)
Loss and loss adjustment expenses			(46,541)	(45,370)
Acquisition expenses	[2]		$ (13,853)	$ (19,915)
Senior notes
Related Party Transaction [Line Items]
Face amount of senior notes						$ 175,000
Stated interest rate (percent)			6.50%			6.50%
Contingently redeemable preference share | Arch Capital Group Limited
Related Party Transaction [Line Items]
Repurchase of preference shares		$ 11,500

[1] Acquisition expenses relating to the ACGL outward quota share agreements referred to above.

[2] Acquisition expenses relating to the ACGL inward quota share agreements referred to above. For the three months ended March 31, 2020 and 2019, the Company incurred ceding fees to Arch, in aggregate, of $4.0 million and $4.2 million, respectively, under these inward retrocession agreements.