Consolidated Statements of Cash Flows - USD ($) $ in Millions		6 Months Ended
		Jun. 30, 2021	Jun. 30, 2020
Statement of Cash Flows [Abstract]
Net income		$ 2,270.1	$ 2,489.5
Adjustments to reconcile net income to net cash provided by operating activities:
Depreciation		129.4	130.3
Amortization of intangible assets		28.5	28.6
Net amortization of fixed-income securities		62.1	42.5
Amortization of equity-based compensation		42.7	45.2
Net realized (gains) losses on securities		(1,047.1)	(337.2)
Net (gains) losses on disposition of property and equipment		0.5	1.8
Changes in:
Premiums receivable		(1,183.5)	(50.1)
Reinsurance recoverables		(237.3)	(275.4)
Prepaid reinsurance premiums		(244.6)	265.2
Deferred acquisition costs		(123.4)	(98.3)
Income taxes		(81.0)	590.6
Unearned premiums		2,051.5	666.8
Loss and loss adjustment expense reserves		2,481.0	406.6
Accounts payable, accrued expenses, and other liabilities		717.8	(2.0)
Other, net		71.7	(25.5)
Net cash provided by operating activities		4,938.4	3,878.6
Purchases:
Fixed maturities		(18,364.5)	(18,193.5)
Equity securities		(416.1)	(671.3)
Sales:
Fixed maturities		8,703.2	13,749.2
Equity securities		590.2	382.1
Maturities, paydowns, calls, and other:
Fixed maturities		3,898.2	4,106.4
Equity securities		67.1	79.0
Net (purchases) sales of short-term investments		3,587.0	(2,883.1)
Net unsettled security transactions		316.6	266.0
Purchases of property and equipment		(98.5)	(110.7)
Acquisition of Protective Insurance Corporation, net of cash, cash equivalents, and restricted cash acquired1		(313.2)	0.0
Sales of property and equipment		11.5	4.8
Net cash used in investing activities		(2,018.5)	(3,271.1)
Cash Flows From Financing Activities
Dividends paid to common shareholders		(2,753.0)	(1,433.9)
Dividends paid to preferred shareholders		(13.4)	(13.4)
Acquisition of treasury shares for restricted stock tax liabilities		(30.4)	(29.1)
Acquisition of treasury shares acquired in open market		(65.0)	0.0
Payment of acquired company debt	[1]	(20.0)	0.0
Acquisition of additional shares of ARX Holding Corp.		0.0	(243.0)
Net proceeds from debt issuances		0.0	986.3
Proceeds from exercise of equity options		0.0	7.3
Net cash used in financing activities		(2,881.8)	(725.8)
Increase (decrease) in cash, cash equivalents, and restricted cash		38.1	(118.3)
Cash, cash equivalents, and restricted cash – January 1		76.5	227.4
Cash, cash equivalents, restricted cash, and restricted cash equivalents – June 30		$ 114.6	$ 109.1

[1] See Note 14 – Acquisition for further discussion.