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Fair Value (Tables)
 6 Months Ended
Jun. 30, 2022
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 June 30, 2022:
  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:    
Available for sale securities:    
Fixed maturities:    
Corporate bonds$7,288,555 $— $7,284,985 $3,570 
Mortgage backed securities698,168 — 698,168 — 
Municipal bonds417,380 — 417,380 — 
Commercial mortgage backed securities1,023,088 — 1,023,088 — 
U.S. government and government agencies4,368,150 4,341,399 26,751 — 
Non-U.S. government securities2,181,943 — 2,181,943 — 
Asset backed securities1,607,745 — 1,604,878 2,867 
Total17,585,029 4,341,399 13,237,193 6,437 
Short-term investments2,227,874 2,049,235 178,639 — 
Equity securities, at fair value772,689 736,343 33,440 2,906 
Derivative instruments (2)122,033 — 122,033 — 
Residential mortgage loans3,929 — 3,929 — 
Fair value option:
Corporate bonds522,707 — 522,707 — 
Non-U.S. government bonds611 — 611 — 
Asset backed securities2,133 — 2,133 — 
Short-term investments39,657 886 38,771 — 
Equity securities14,489 10,097 — 4,392 
Other investments178,461 — 145,130 33,331 
Other investments measured at net asset value (1)876,310 
Total1,634,368 10,983 709,352 37,723 
Total assets measured at fair value$22,345,922 $7,137,960 $14,284,586 $47,066 
Liabilities measured at fair value:    
Other liabilities$(16,205)$— $— $(16,205)
Derivative instruments (2)(75,147)— (75,147)— 
Total liabilities measured at fair value$(91,352)$— $(75,147)$(16,205)

(1)    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.
(2)    See note 9.
The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2021:
  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:
Available for sale securities:
Fixed maturities:
Corporate bonds$6,553,333 $— $6,553,320 $13 
Mortgage backed securities408,477 — 408,477 — 
Municipal bonds404,666 — 404,666 — 
Commercial mortgage backed securities1,046,484 — 1,046,484 — 
U.S. government and government agencies4,772,764 4,744,517 28,247 — 
Non-U.S. government securities2,120,294 — 2,120,294 — 
Asset backed securities2,692,091 — 2,688,744 3,347 
Total17,998,109 4,744,517 13,250,232 3,360 
Short-term investments1,734,716 1,052,822 681,894 — 
Equity securities, at fair value1,804,170 1,762,864 38,388 2,918 
Derivative instruments (2)127,121 — 127,121 — 
Residential mortgage loans49,847 — 49,847 — 
Fair value option:
Corporate bonds388,546 — 388,546 — 
Non-U.S. government bonds23,785 — 23,785 — 
Asset backed securities4,367 — 4,367 — 
Short-term investments97,806 528 97,278 — 
Equity securities26,493 21,745 — 4,748 
Other investments310,798 20,352 262,465 27,981 
Other investments measured at net asset value (1)1,121,755 
Total1,973,550 42,625 776,441 32,729 
Total assets measured at fair value$23,687,513 $7,602,828 $14,923,923 $39,007 
Liabilities measured at fair value:
Other liabilities$(16,960)$— $— $(16,960)
Derivative instruments (2)(54,224)— (54,224)— 
Total liabilities measured at fair value$(71,184)$— $(54,224)$(16,960)

(1)    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.
(2)    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		Other Liabilities
Three Months Ended June 30, 2022  
Balance at beginning of period$3,152 $3,570 $— $22,602 $4,511 $2,768 $(17,591)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)(1)— — 27 (119)(89)(97)
Included in other comprehensive income(85)— — — — — 1,483 
Purchases, issuances, sales and settlements
Purchases— — — 10,702 — 227 — 
Issuances— — — — — — — 
Sales— — — — — — — 
Settlements(199)— — — — — — 
Transfers in and/or out of Level 3— — — — — — — 
Balance at end of period$2,867 $3,570 $— $33,331 $4,392 $2,906 $(16,205)
Three Months Ended June 30, 2021  
Balance at beginning of period$3,472 $13 $989 $67,930 $71,176 $43,112 $(465)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)12 — 9 633 2,502 922 (1)
Included in other comprehensive income(57)— — — — — — 
Purchases, issuances, sales and settlements
Purchases— — — 5,638 — 5,102 — 
Issuances— — — — — — — 
Sales— — — (301)— — — 
Settlements(3)— — — — — — 
Transfers in and/or out of Level 3— — — — — — — 
Balance at end of period$3,424 $13 $998 $73,900 $73,678 $49,136 $(466)
Six Months Ended June 30, 2022  
Balance at beginning of year$3,347 $13 $— $27,981 $4,748 $2,918 $(16,960)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)9 — — 34 (356)(236)(195)
Included in other comprehensive income(145)— — — — — 950 
Purchases, issuances, sales and settlements
Purchases— — — 10,770 — 227 — 
Issuances— — — — — — — 
Sales (3)— — — (2,471)— (3)— 
Settlements(344)— — (2,983)— — — 
Transfers in and/or out of Level 3— 3,557 — — — — — 
Balance at end of period$2,867 $3,570 $— $33,331 $4,392 $2,906 $(16,205)
Six Months Ended June 30, 2021  
Balance at beginning of year$3,426 $13 $985 $67,103 $68,988 $42,015 $(461)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)(56)— 13 881 4,690 1,826 (5)
Included in other comprehensive income57 — — — — — — 
Purchases, issuances, sales and settlements
Purchases— — — 13,003 — 5,295 — 
Issuances— — — — — — — 
Sales— — — (7,087)— — — 
Settlements(3)— — — — — — 
Transfers in and/or out of Level 3— — — — — — — 
Balance at end of period$3,424 $13 $998 $73,900 $73,678 $49,136 $(466)
(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.
(2)    Gains or losses were included in net realized gains (losses).