Consolidated Statements of Cash Flows - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Statement of Cash Flows [Abstract]
Net income	$ 3,980.0	$ 2,621.0	$ 1,598.1
Adjustments to reconcile net income to net cash provided by operating activities:
Depreciation	239.8	190.4	169.9
Amortization of intangible assets	66.3	72.0	66.2
Net amortization of fixed-income securities	33.3	34.3	86.2
Amortization of equity-based compensation	90.2	77.2	95.4
Net realized (gains) losses on securities	(1,029.2)	405.5	(49.6)
Net (gains) losses on disposition of property and equipment	11.0	32.1	7.2
Other (gains) losses	0.0	0.0	1.0
Changes in:
Premiums receivable	(1,010.2)	(1,074.6)	(913.2)
Reinsurance recoverables	(682.8)	(422.7)	(388.6)
Prepaid reinsurance premiums	(316.8)	(106.4)	(32.8)
Deferred acquisition costs	(104.9)	(171.1)	(129.3)
Income taxes	227.2	(158.7)	(172.6)
Unearned premiums	1,702.3	1,783.0	1,434.9
Loss and loss adjustment expense reserves	2,704.6	2,313.9	1,718.8
Accounts payable, accrued expenses, and other liabilities	611.6	746.6	400.0
Other, net	(260.8)	(57.7)	(134.8)
Net cash provided by operating activities	6,261.6	6,284.8	3,756.8
Purchases:
Fixed maturities	(28,765.2)	(21,153.0)	(14,587.8)
Equity securities	(379.9)	(538.8)	(255.6)
Sales:
Fixed maturities	18,412.7	7,835.6	5,382.5
Equity securities	471.4	823.5	252.9
Maturities, paydowns, calls, and other:
Fixed maturities	6,145.5	5,099.8	5,215.8
Equity securities	49.9	26.6	50.0
Net sales of short-term investments	31.5	1,116.3	727.6
Net unsettled security transactions	6.0	11.7	(33.6)
Purchases of property and equipment	(363.5)	(266.0)	(155.7)
Sales of property and equipment	53.3	9.4	15.3
Acquisition of an insurance company, net of cash acquired	0.0	0.0	(18.1)
Net cash used in investing activities	(4,338.3)	(7,034.9)	(3,406.7)
Cash Flows From Financing Activities
Dividends paid to common shareholders	(1,643.2)	(654.9)	(395.4)
Dividends paid to preferred shareholders	(26.8)	(13.5)	0.0
Acquisition of treasury shares for restricted stock tax liabilities	(84.4)	(78.6)	(57.6)
Acquisition of treasury shares acquired in open market	(6.9)	(0.4)	(4.9)
Acquisition of additional shares of ARX Holding Corp.	(11.2)	(296.9)	0.0
Net proceeds from debt issuance	0.0	1,134.0	841.1
Net proceeds from issuance of Serial Preferred Shares, Series B	0.0	493.9	0.0
Payments of debt	0.0	(37.1)	(49.0)
Proceeds from exercise of equity options	1.6	3.3	0.5
Redemption/reacquisition of subordinated debt	0.0	0.0	(635.6)
Net cash provided by (used in) financing activities	(1,770.9)	549.8	(300.9)
Effect of exchange rate changes on cash	0.0	0.0	(0.3)
Increase (decrease) in cash, cash equivalents, and restricted cash	152.4	(200.3)	48.9
Cash, cash equivalents, and restricted cash - beginning of year	75.0	275.3	226.4
Cash, cash equivalents, and restricted cash - end of year	$ 227.4	$ 75.0	$ 275.3