Segment Information - Income Statement Information (Details) $ in Millions	12 Months Ended
	Dec. 31, 2022 USD ($) segment	Dec. 31, 2021 USD ($)	Dec. 31, 2020 USD ($)
Segment Reporting [Abstract]
Number of operating segments | segment	3
Segment reporting information
Earned insurance premiums	$ 1,076.7	$ 664.2	$ 22.8
Net investment income	124.4	82.5	131.0
Net realized and unrealized investment gains (losses)	(98.5)	134.2	30.8
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	(93.0)	(380.3)	686.0
Commission revenues	11.5	9.6	8.3
Other revenues	136.8	104.2	16.7
Total revenues	1,157.9	614.4	895.6
Loss and loss adjustment expenses	536.4	314.8
Insurance acquisition expenses	250.6	186.3	7.0
Cost of sales	98.6	69.3	11.3
General and administrative expenses	376.2	292.5	207.9
Amortization of other intangible assets	5.2	4.6	1.6
Interest expense	40.3	20.5	7.4
Total expenses	1,307.3	888.0	235.2
Pre-tax income (loss)	(149.4)	(273.6)	660.4
United Kingdom
Segment reporting information
Earned insurance premiums		459.3
BERMUDA
Segment reporting information
Earned insurance premiums		178.0
HG Global-BAM
Segment reporting information
Earned insurance premiums	33.3	26.9	22.8
Net investment income	21.5	17.5	19.5
Net realized and unrealized investment gains (losses)	(105.8)	(22.9)	23.7
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0.0	0.0	0.0
Commission revenues	0.0	0.0	0.0
Other revenues	4.6	1.5	2.5
Total revenues	(46.4)	23.0	68.5
Loss and loss adjustment expenses	0.0	0.0
Insurance acquisition expenses	11.2	8.3	7.0
Cost of sales	0.0	0.0	0.0
General and administrative expenses	69.1	57.1	56.8
Amortization of other intangible assets	0.0	0.0	0.0
Interest expense	8.3	0.0	0.0
Total expenses	88.6	65.4	63.8
Pre-tax income (loss)	(135.0)	(42.4)	4.7
Ark
Segment reporting information
Earned insurance premiums	1,043.4	637.3	0.0
Net investment income	16.3	2.9	0.0
Net realized and unrealized investment gains (losses)	(55.2)	16.5	0.0
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0.0	0.0
Commission revenues	0.0	0.0
Other revenues	5.0	11.8	0.0
Total revenues	1,009.5	668.5	0.0
Loss and loss adjustment expenses	536.4	314.8	0.0
Insurance acquisition expenses	239.4	178.0	0.0
Cost of sales	0.0	0.0
General and administrative expenses	123.5	115.5	0.0
Amortization of other intangible assets	0.0	0.0
Interest expense	15.1	7.3	0.0
Total expenses	914.4	615.6	0.0
Pre-tax income (loss)	95.1	52.9
Ark | United Kingdom
Segment reporting information
Earned insurance premiums	638.5
Ark | BERMUDA
Segment reporting information
Earned insurance premiums	404.9
Kudu
Segment reporting information
Earned insurance premiums	0.0	0.0	0.0
Net investment income	54.4	43.9	29.5
Net realized and unrealized investment gains (losses)	64.1	89.9	15.9
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0.0	0.0	0.0
Commission revenues	0.0	0.0	0.0
Other revenues	0.0	0.2	0.3
Total revenues	118.5	134.0	45.7
Loss and loss adjustment expenses	0.0
Insurance acquisition expenses	0.0	0.0	0.0
Cost of sales	0.0	0.0	0.0
General and administrative expenses	14.4	14.5	11.8
Amortization of other intangible assets	0.3	0.3	0.3
Interest expense	15.0	11.7	6.0
Total expenses	29.7	26.5	18.1
Pre-tax income (loss)	88.8	107.5	27.6
Other Operations
Segment reporting information
Earned insurance premiums	0.0	0.0	0.0
Net investment income	32.2	18.2	82.0
Net realized and unrealized investment gains (losses)	(1.6)	50.7	(8.8)
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	(93.0)	(380.3)	686.0
Commission revenues	11.5	9.6	8.3
Other revenues	127.2	90.7	13.9
Total revenues	76.3	(211.1)	781.4
Loss and loss adjustment expenses	0.0	0.0
Insurance acquisition expenses	0.0	0.0	0.0
Cost of sales	98.6	69.3	11.3
General and administrative expenses	169.2	105.4	139.3
Amortization of other intangible assets	4.9	4.3	1.3
Interest expense	1.9	1.5	1.4
Total expenses	274.6	180.5	153.3
Pre-tax income (loss)	$ (198.3)	$ (391.6)	$ 628.1