Consolidated Statements of Cash Flows - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016
Statement of Cash Flows [Abstract]
Net income	$ 2,621.0	$ 1,598.1	$ 1,057.2
Adjustments to reconcile net income to net cash provided by operating activities:
Depreciation	190.4	169.9	137.4
Amortization of intangible assets	72.0	66.2	62.1
Net amortization of fixed-income securities	34.3	86.2	77.2
Amortization of equity-based compensation	77.2	95.4	85.2
Net realized (gains) losses on securities	405.5	(49.6)	(51.1)
Net (gains) losses on disposition of property and equipment	32.1	7.2	6.6
Other (gains) losses	0.0	1.0	(1.6)
Net loss on exchange transaction	0.0	0.0	4.5
Changes in:
Premiums receivable	(1,074.6)	(913.2)	(518.5)
Reinsurance recoverables	(422.7)	(388.6)	(388.2)
Prepaid reinsurance premiums	(106.4)	(32.8)	48.8
Deferred acquisition costs	(171.1)	(129.3)	(103.8)
Income taxes	(158.7)	(172.6)	(55.7)
Unearned premiums	1,783.0	1,434.9	830.7
Loss and loss adjustment expense reserves	2,313.9	1,718.8	1,323.2
Accounts payable, accrued expenses, and other liabilities	746.6	400.0	308.9
Other, net	(57.7)	(134.8)	(90.2)
Net cash provided by operating activities	6,284.8	3,756.8	2,732.7
Purchases:
Fixed maturities	(21,153.0)	(14,587.8)	(11,610.6)
Equity securities	(538.8)	(255.6)	(434.2)
Sales:
Fixed maturities	7,835.6	5,382.5	5,694.9
Equity securities	823.5	252.9	484.6
Maturities, paydowns, calls, and other:
Fixed maturities	5,099.8	5,215.8	4,907.4
Equity securities	26.6	50.0	0.0
Net sales (purchases) of short-term investments	1,116.3	727.6	(1,357.2)
Net unsettled security transactions	11.7	(33.6)	50.9
Purchases of property and equipment	(266.0)	(155.7)	(215.0)
Sales of property and equipment	9.4	15.3	6.2
Acquisition of additional shares of ARX Holding Corp.	(296.9)	0.0	0.0
Acquisition of an insurance company, net of cash acquired	0.0	(18.1)	0.0
Net cash disposed in exchange transaction	0.0	0.0	(7.7)
Net cash used in investing activities	(7,331.8)	(3,406.7)	(2,480.7)
Cash Flows From Financing Activities
Net proceeds from debt issuance	1,134.0	841.1	495.6
Net proceeds from issuance of Serial Preferred Shares, Series B	493.9	0.0	0.0
Payments of debt	37.1	49.0	25.5
Dividends paid to common shareholders	654.9	395.4	519.0
Dividends paid to preferred shareholders	(13.5)	0.0	0.0
Proceeds from exercise of equity options	3.3	0.5	0.0
Acquisition of treasury shares for restricted stock tax liabilities	(78.6)	(57.6)	(25.1)
Acquisition of treasury shares acquired in open market	(0.4)	(4.9)	(167.4)
Redemption/reacquisition of subordinated debt	0.0	(635.6)	(18.2)
Tax benefit from vesting of equity-based compensation	0.0	0.0	9.2
Net cash provided by (used in) financing activities	846.7	(300.9)	(250.4)
Effect of exchange rate changes on cash	0.0	(0.3)	0.4
Increase (decrease) in cash, cash equivalents, and restricted cash	(200.3)	48.9	2.0
Cash, cash equivalents, and restricted cash - Beginning of year	275.3	226.4	224.4
Cash, cash equivalents, and restricted cash - End of year	$ 75.0	$ 275.3	$ 226.4