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Fair Value (Tables)
 9 Months Ended
Sep. 30, 2020
Fair Value Disclosures [Abstract]  
Fair value hierarchy
The following table presents the Company’s financial assets and liabilities measured at fair value by level at September 30, 2020:
  Estimated Fair Value Measurements Using:
 Estimated
Fair
Value		Quoted Prices in
Active Markets
for Identical
Assets
(Level 1)		Significant
Other
Observable
Inputs
(Level 2)		Significant
Unobservable
Inputs
(Level 3)
Assets measured at fair value (1):    
Available for sale securities:    
Fixed maturities:    
Corporate bonds$7,965,599 $— $7,965,586 $13 
Mortgage backed securities717,081 — 716,873 208 
Municipal bonds527,410 — 527,410 — 
Commercial mortgage backed securities374,360 — 374,360 — 
U.S. government and government agencies4,861,349 4,715,551 145,798 — 
Non-U.S. government securities2,302,646 — 2,302,646 — 
Asset backed securities1,767,192 — 1,763,845 3,347 
Total18,515,637 4,715,551 13,796,518 3,568 
Short-term investments2,039,097 2,013,582 25,515 — 
Equity securities, at fair value1,502,015 1,452,713 6,616 42,686 
Derivative instruments (4)130,494 — 130,494 — 
Fair value option:
Corporate bonds780,237 — 779,273 964 
Non-U.S. government bonds44,963 — 44,963 — 
Mortgage backed securities13,026 — 13,026 — 
Municipal bonds— — — — 
Commercial mortgage backed securities1,150 — 1,150 — 
Asset backed securities175,790 — 175,790 — 
U.S. government and government agencies4,363 4,252 111 — 
Short-term investments468,704 360,883 107,821 — 
Equity securities91,445 27,766 156 63,523 
Other investments1,152,517 52,080 1,034,251 66,186 
Other investments measured at net asset value (2)1,017,380 
Total3,749,575 444,981 2,156,541 130,673 
Total assets measured at fair value$25,936,818 $8,626,827 $16,115,684 $176,927 
Liabilities measured at fair value:    
Contingent consideration liabilities$(630)$— $— $(630)
Securities sold but not yet purchased (3)(24,909)— (24,909)— 
Derivative instruments (4)(82,457)— (82,457)— 
Total liabilities measured at fair value$(107,996)$— $(107,366)$(630)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”
(2)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.
(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.
(4)    See note 9.
The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2019:
  Estimated Fair Value Measurements Using:
 Estimated
Fair
Value		Quoted Prices in
Active Markets
for Identical
Assets
(Level 1)		Significant
Other
Observable
Inputs
(Level 2)		Significant
Unobservable
Inputs
(Level 3)
Assets measured at fair value (1):
Available for sale securities:
Fixed maturities:
Corporate bonds$6,406,591 $— $6,397,740 $8,851 
Mortgage backed securities562,309 — 562,055 254 
Municipal bonds881,926 — 881,926 — 
Commercial mortgage backed securities733,108 — 733,108 — 
U.S. government and government agencies4,916,592 4,805,581 111,011 — 
Non-U.S. government securities2,078,757 — 2,078,757 — 
Asset backed securities1,683,753 — 1,678,791 4,962 
Total17,263,036 4,805,581 12,443,388 14,067 
Short-term investments956,546 904,804 51,742 — 
Equity securities, at fair value850,283 789,596 4,798 55,889 
Derivative instruments (4)48,946 — 48,946 — 
Fair value option:
Corporate bonds488,402 — 487,470 932 
Non-U.S. government bonds50,465 — 50,465 — 
Mortgage backed securities11,947 — 11,947 — 
Municipal bonds377 — 377 — 
Commercial mortgage backed securities1,134 — 1,134 — 
Asset backed securities200,163 — 200,163 — 
U.S. government and government agencies1,962 1,852 110 — 
Short-term investments377,014 333,320 43,694 — 
Equity securities102,697 43,962 641 58,094 
Other investments1,418,273 53,287 1,296,169 68,817 
Other investments measured at net asset value (2)1,011,043 
Total3,663,477 432,421 2,092,170 127,843 
Total assets measured at fair value$22,782,288 $6,932,402 $14,641,044 $197,799 
Liabilities measured at fair value:
Contingent consideration liabilities$(7,998)$— $— $(7,998)
Securities sold but not yet purchased (3)(66,257)— (66,257)— 
Derivative instruments (4)(39,750)— (39,750)— 
Total liabilities measured at fair value$(114,005)$— $(106,007)$(7,998)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”
(2)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.
(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.
(4)    See note 9.
Rollforward of Level 3 investments
The following table presents a reconciliation of the beginning and ending balances for all financial assets and liabilities measured at fair value on a recurring basis using Level 3 inputs:
AssetsLiabilities
sAvailable For SaleFair Value OptionFair Value
 Structured Securities (1)Corporate
Bonds		Corporate
Bonds		Other
Investments		Equity
Securities		Equity
Securities		Contingent Consideration Liabilities
Three Months Ended September 30, 2020  
Balance at beginning of period$3,450 $857 $998 $46,453 $61,447 $51,981 $(1,250)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)(75)(5,872)(34)885 2,076 (946)— 
Included in other comprehensive income191 6,936 — — — — — 
Purchases, issuances, sales and settlements
Purchases— — — 22,436 — — — 
Issuances— — — — — — — 
Sales— — — (3,588)— (8,349)— 
Settlements(11)— — — — — 620 
Transfers in and/or out of Level 3— (1,908)— — — — — 
Balance at end of period$3,555 $13 $964 $66,186 $63,523 $42,686 $(630)
Three Months Ended September 30, 2019  
Balance at beginning of period$290 $7,642 $26,103 $95,273 $56,145 $51,212 $(7,825)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)— — (1,227)(411)127 (26)(79)
Included in other comprehensive income— (301)— — — — — 
Purchases, issuances, sales and settlements
Purchases— — — 3,713 — 12,119 — 
Issuances— — — — — — — 
Sales— — (2,097)(80)— (27,982)— 
Settlements(18)(456)— — — — 560 
Transfers in and/or out of Level 35,449 1,860 — (13,052)— — — 
Balance at end of period$5,721 $8,745 $22,779 $85,443 $56,272 $35,323 $(7,344)
Nine Months Ended September 30, 2020  
Balance at beginning of year$5,216 $8,851 $932 $68,817 $58,094 $55,889 $(7,998)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)(130)(5,865)(34)(129)5,429 7,132 (72)
Included in other comprehensive income(118)397 — — — — — 
Purchases, issuances, sales and settlements
Purchases— — 66 22,460 — 3,464 — 
Issuances— — — — — — — 
Sales— — — (27,946)— (23,799)— 
Settlements(1,413)(1,462)— — — — 7,440 
Transfers in and/or out of Level 3— (1,908)— 2,984 — — — 
Balance at end of period$3,555 $13 $964 $66,186 $63,523 $42,686 $(630)
Nine Months Ended September 30, 2019  
Balance at beginning of year$313 $8,141 $5,758 $62,705 $— $— $(66,665)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)1,757 — (1,566)(11,727)127 (26)(1,410)
Included in other comprehensive income5 (317)— — — — — 
Purchases, issuances, sales and settlements
Purchases— 429 — 3,713 — 12,119 — 
Issuances— — — — — — (548)
Sales(1,757)— (5,332)(228)— (27,982)— 
Settlements(46)(1,368)— (600)— — 61,279 
Transfers in and/or out of Level 35,449 1,860 23,919 31,580 56,145 51,212 — 
Balance at end of period$5,721 $8,745 $22,779 $85,443 $56,272 $35,323 $(7,344)
(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.
(2)    Gains or losses were included in net realized gains (losses).