Consolidated Statements of Cash Flows - USD ($) $ in Millions	9 Months Ended
	Sep. 30, 2019	Sep. 30, 2018
Statement of Cash Flows [Abstract]
Net income	$ 2,905.4	$ 2,361.2
Adjustments to reconcile net income to net cash provided by operating activities:
Depreciation	171.0	137.8
Amortization of intangible assets	51.7	54.0
Net amortization of fixed-income securities	14.1	29.7
Amortization of equity-based compensation	64.7	54.0
Net realized (gains) losses on securities	(659.8)	(166.7)
Net (gains) losses on disposition of property and equipment	(0.1)	7.4
Changes in:
Premiums receivable	(1,190.1)	(1,354.1)
Reinsurance recoverables	(602.3)	(217.1)
Prepaid reinsurance premiums	(149.1)	(176.3)
Deferred acquisition costs	(142.1)	(182.2)
Income taxes	179.7	25.0
Unearned premiums	1,840.0	2,105.7
Loss and loss adjustment expense reserves	1,969.2	1,533.9
Accounts payable, accrued expenses, and other liabilities	920.5	1,032.8
Other, net	(239.4)	(43.6)
Net cash provided by operating activities	5,133.4	5,201.5
Purchases:
Fixed maturities	(20,105.3)	(14,430.6)
Equity securities	(291.9)	(234.9)
Sales:
Fixed maturities	12,112.9	4,659.6
Equity securities	175.7	773.5
Maturities, paydowns, calls, and other:
Fixed maturities	4,236.7	3,911.5
Fixed maturities	22.8	15.0
Net sales of short-term investments	356.8	91.9
Net unsettled security transactions	280.6	11.0
Purchases of property and equipment	(281.2)	(164.8)
Sales of property and equipment	39.9	8.1
Acquisition of additional shares of ARX Holding Corp.	(11.2)	(296.9)
Net cash used in investing activities	(3,464.2)	(5,656.6)
Cash Flows From Financing Activities
Dividends paid to common shareholders	(1,584.7)	(654.9)
Dividends paid to preferred shareholders	(26.8)	(13.5)
Acquisition of treasury shares for restricted stock tax liabilities	(81.2)	(78.3)
Acquisition of treasury shares acquired in open market	(6.9)	(0.4)
Proceeds from exercise of equity options	1.6	3.3
Net proceeds from issuance of Serial Preferred Shares, Series B	0.0	493.9
Net proceeds from debt issuances	0.0	589.5
Payments of debt	0.0	(37.1)
Net cash provided by (used in) financing activities	(1,698.0)	302.5
Decrease in cash, cash equivalents, and restricted cash	(28.8)	(152.6)
Cash, cash equivalents, and restricted cash – January 1	75.0	275.3
Cash, cash equivalents, and restricted cash – September 30	$ 46.2	$ 122.7