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Consolidated Statements of Cash Flows - USD ($)
$ in Millions
 12 Months Ended
Dec. 31, 2017
Dec. 31, 2016
Dec. 31, 2015
Net income $ 1,598.1 $ 1,057.2 $ 1,300.5
Adjustments to reconcile net income to net cash provided by operating activities:      
Depreciation 169.9 137.4 103.7
Amortization of intangible assets 66.2 62.1 46.8
Net amortization of fixed-income securities 86.2 77.2 98.4
Amortization of equity-based compensation 95.4 85.2 66.2
Net realized (gains) losses on securities (49.6) (51.1) (112.7)
Net (gains) losses on disposition of property and equipment 7.2 6.6 2.0
Other (gains) losses 1.0 (1.6) 0.9
Net loss on exchange transaction 0.0 4.5 0.0
Changes in:      
Premiums receivable (913.2) (518.5) (421.1)
Reinsurance recoverables (388.6) (388.2) (202.6)
Prepaid reinsurance premiums (32.8) 48.8 32.5
Deferred acquisition costs (129.3) (103.8) (42.3)
Income taxes (172.6) (55.7) (107.2)
Unearned premiums 1,434.9 830.7 632.4
Loss and loss adjustment expense reserves 1,718.8 1,323.2 917.7
Accounts payable, accrued expenses, and other liabilities 400.0 308.9 37.9
Other, net (134.8) (90.2) (60.2)
Net cash provided by operating activities 3,756.8 2,732.7 2,292.9
Purchases:      
Fixed maturities (14,587.8) (11,610.6) (9,311.1)
Equity securities (255.6) (434.2) (647.1)
Sales:      
Fixed maturities 5,382.5 5,694.9 4,913.5
Equity securities 252.9 484.6 402.4
Maturities, paydowns, calls, and other:      
Fixed maturities 5,215.8 4,907.4 3,579.5
Equity securities 50.0 0.0 12.0
Net sales (purchases) of short-term investments 727.6 (1,357.2) 20.5
Net unsettled security transactions (33.6) 50.9 (8.2)
Purchases of property and equipment (155.7) (215.0) (130.7)
Sales of property and equipment 15.3 6.2 10.6
Net cash disposed in exchange transaction 0.0 (7.7) 0.0
Acquisition of additional shares of ARX Holding Corp. 0.0 0.0 (12.6)
Net cash used in investing activities (3,406.7) (2,480.7) (1,923.9)
Cash Flows From Financing Activities      
Proceeds from exercise of equity options 0.5 0.0 0.2
Net proceeds from debt issuance 841.1 495.6 382.0
Payments of debt (49.0) (25.5) (20.4)
Redemption/reacquisition of subordinated debt (635.6) (18.2) (19.3)
Dividends paid to shareholders (395.4) (519.0) (403.6)
Acquisition of treasury shares for restricted stock tax liabilities (57.6) (25.1) (30.6)
Acquisition of treasury shares acquired in open market (4.9) (167.4) (177.9)
Tax benefit from vesting of equity-based compensation 0.0 9.2 16.8
Net cash used in financing activities (300.9) (250.4) (252.8)
Effect of exchange rate changes on cash (0.3) 0.4 (0.2)
Increase in cash, cash equivalents, and restricted cash 48.9 2.0 116.0
Cash, cash equivalents, and restricted cash - Beginning of year 226.4 224.4 108.4
Cash, cash equivalents, and restricted cash - End of year 275.3 226.4 224.4
Insurance Company      
Maturities, paydowns, calls, and other:      
Acquisition of business, net of cash acquired [1] (18.1) 0.0 0.0
ARX Holding Corp.      
Maturities, paydowns, calls, and other:      
Acquisition of business, net of cash acquired $ 0.0 $ 0.0 $ (752.7)
[1] See Note 1 – Reporting and Accounting Policies for further information.