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Consolidated Statements of Cash Flows - USD ($)
$ in Millions
9 Months Ended
Sep. 30, 2016
Sep. 30, 2015
Statement of Cash Flows [Abstract]    
Net income $ 659.1 $ 950.6
Adjustments to reconcile net income to net cash provided by operating activities:    
Depreciation 94.6 76.1
Amortization of intangible assets 46.6 31.2
Amortization of fixed-income securities 57.1 71.2
Amortization of equity-based compensation 64.6 45.9
Net realized (gains) losses on securities (29.0) (93.2)
Net (gains) losses on disposition of property and equipment 4.1 0.5
(Gains) losses on extinguishment of debt (1.6) 0.9
Net loss on exchange transaction 4.5 0.0
Changes in:    
Premiums receivable (752.8) (573.2)
Reinsurance recoverables (405.1) (128.8)
Prepaid reinsurance premiums 44.9 10.1
Deferred acquisition costs (128.0) (69.0)
Income taxes (121.2) (92.1)
Unearned premiums 1,154.6 982.7
Loss and loss adjustment expense reserves 1,183.2 705.8
Accounts payable, accrued expenses, and other liabilities 464.8 218.7
Increase (Decrease) in Restricted Cash (22.0) 0.0
Other, net (58.8) 23.0
Net cash provided by operating activities 2,259.6 2,160.4
Purchases:    
Fixed maturities (7,364.6) (7,106.7)
Equity securities (367.1) (461.3)
Sales:    
Fixed maturities 4,746.1 3,639.8
Equity securities 278.2 251.8
Maturities, paydowns, calls, and other:    
Fixed maturities 4,189.0 2,469.4
Equity securities 0.0 12.0
Net sales (purchases) of short-term investments (3,665.2) 60.4
Net unsettled security transactions 208.4 118.6
Sales of property and equipment 4.5 8.7
Purchases of property and equipment (162.1) (86.6)
Net cash acquired in exchange transaction 8.5 0.0
Acquisition of ARX Holding Corp., net of cash acquired 0.0 (752.7)
Acquisition of additional shares of ARX Holding Corp. 0.0 (12.6)
Net cash used in investing activities (2,124.3) (1,859.2)
Cash Flows From Financing Activities    
Tax benefit from vesting of equity-based compensation 8.0 15.0
Net proceeds from debt issuance 495.6 382.0
Payments of debt (19.2) (13.6)
Reacquisition of debt 18.2 19.3
Dividends paid to shareholders (519.0) (403.6)
Acquisition of treasury shares (163.6) (174.9)
Net cash used in financing activities (216.4) (214.4)
Effect of exchange rate changes on cash 0.4 (0.7)
Increase (decrease) in cash (80.7) 86.1
Cash, January 1 224.1 108.4
Cash, September 30 $ 143.4 $ 194.5