Loss and Loss Adjustment Expense Reserves (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Liability for Unpaid Claims and Claims Adjustment Expense [Roll Forward]
Gross beginning balance	$ 1,022.1	$ 760.0	$ 894.7	$ 696.0
Less: beginning reinsurance recoverable on unpaid losses	(375.5)	(425.3)	(428.9)	(433.4)
Net loss and LAE reserves	646.6	334.7	465.8	262.6
Loss and LAE incurred relating to:
Current year losses	222.9	141.9	491.8	269.0
Prior year losses	(9.2)	(12.7)	(35.6)	(21.2)
Net incurred losses and LAE	213.7	129.2	456.2	247.8
Loss and LAE paid relating to:
Current year losses	(6.1)	(9.0)	(20.8)	(11.5)
Prior year losses	(37.0)	(20.3)	(130.8)	(62.1)
Net paid loss and LAE	(43.1)	(29.3)	(151.6)	(73.6)
Change in TPC providers’ participation	0.0	0.0	57.5	(2.2)
Foreign currency translation and other adjustments to loss and LAE reserves	(9.2)	(1.2)	(19.9)	(1.2)
Net ending balance	808.0	433.4	808.0	433.4
Plus: ending reinsurance recoverable on unpaid losses	521.4	457.5	521.4	457.5
Gross ending balance	1,329.4	890.9	1,329.4	890.9
Liability for Claims and Claims Adjustment Expense [Line Items]
Loss and loss adjustment expense reserves	521.4	457.5	521.4	457.5	$ 428.9	$ 433.4
Ark
Liability for Unpaid Claims and Claims Adjustment Expense [Roll Forward]
Gross beginning balance			894.7
Loss and LAE paid relating to:
Gross ending balance	1,329.4		1,329.4
Liability for Claims and Claims Adjustment Expense [Line Items]
Reinsurance recoverables	550.9	465.6	550.9	465.6	$ 448.4
TPC Providers | Ark
Liability for Claims and Claims Adjustment Expense [Line Items]
Reinsurance recoverables	168.0	299.9	168.0	299.9
TPC Providers
Liability for Unpaid Claims and Claims Adjustment Expense [Roll Forward]
Less: beginning reinsurance recoverable on unpaid losses	(182.4)	(314.6)
Loss and LAE paid relating to:
Plus: ending reinsurance recoverable on unpaid losses	276.8	319.2	276.8	319.2
Liability for Claims and Claims Adjustment Expense [Line Items]
Loss and loss adjustment expense reserves	$ 276.8	319.2	$ 276.8	319.2
Reinsurance recoverables		$ 299.9		$ 299.9
Ark | TPC Providers
Liability for Claims and Claims Adjustment Expense [Line Items]
Percent of underwriting capital provided by third parties						42.80%	58.30%	57.60%