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Fair Value - Fair Value Hierarchy (Details) - Recurring - USD ($) $ in Thousands | Sep. 30, 2020 | Dec. 31, 2019
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Quoted Prices in Active Markets for Identical Assets (Level 1) |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | $ 8,626,827 | $ 6,932,402
Liabilities measured at fair value |  | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Contingent consideration liability |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities measured at fair value |  | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Securities sold but not yet purchased |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities measured at fair value | [1] | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Derivative instruments |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities measured at fair value |  | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 4,715,551 | 4,805,581
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | Corporate bonds |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | Mortgage backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | Municipal bonds |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | Commercial mortgage backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | US government and government agencies |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 4,715,551 | 4,805,581
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | Non-US government securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | Asset backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Short-term investments |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 2,013,582 | 904,804
Quoted Prices in Active Markets for Identical Assets (Level 1) | Equity securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 1,452,713 | 789,596
Quoted Prices in Active Markets for Identical Assets (Level 1) | Derivative instruments |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 444,981 | 432,421
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Corporate bonds |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Mortgage backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Municipal bonds |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Commercial mortgage backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | US government and government agencies |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 4,252 | 1,852
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Non-US government securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Asset backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Short-term investments |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 360,883 | 333,320
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Equity securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 27,766 | 43,962
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Other investments fair value option |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 52,080 | 53,287
Significant Other Observable Inputs (Level 2) |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 16,115,684 | 14,641,044
Liabilities measured at fair value |  | (107,366) | (106,007)
Significant Other Observable Inputs (Level 2) | Contingent consideration liability |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities measured at fair value |  | 0 | 0
Significant Other Observable Inputs (Level 2) | Securities sold but not yet purchased |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities measured at fair value | [1] | (24,909) | (66,257)
Significant Other Observable Inputs (Level 2) | Derivative instruments |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities measured at fair value |  | (82,457) | (39,750)
Significant Other Observable Inputs (Level 2) | Fixed maturities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 13,796,518 | 12,443,388
Significant Other Observable Inputs (Level 2) | Fixed maturities | Corporate bonds |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 7,965,586 | 6,397,740
Significant Other Observable Inputs (Level 2) | Fixed maturities | Mortgage backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 716,873 | 562,055
Significant Other Observable Inputs (Level 2) | Fixed maturities | Municipal bonds |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 527,410 | 881,926
Significant Other Observable Inputs (Level 2) | Fixed maturities | Commercial mortgage backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 374,360 | 733,108
Significant Other Observable Inputs (Level 2) | Fixed maturities | US government and government agencies |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 145,798 | 111,011
Significant Other Observable Inputs (Level 2) | Fixed maturities | Non-US government securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 2,302,646 | 2,078,757
Significant Other Observable Inputs (Level 2) | Fixed maturities | Asset backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 1,763,845 | 1,678,791
Significant Other Observable Inputs (Level 2) | Short-term investments |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 25,515 | 51,742
Significant Other Observable Inputs (Level 2) | Equity securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 6,616 | 4,798
Significant Other Observable Inputs (Level 2) | Derivative instruments |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 130,494 | 48,946
Significant Other Observable Inputs (Level 2) | Fair value option |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 2,156,541 | 2,092,170
Significant Other Observable Inputs (Level 2) | Fair value option | Corporate bonds |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 779,273 | 487,470
Significant Other Observable Inputs (Level 2) | Fair value option | Mortgage backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 13,026 | 11,947
Significant Other Observable Inputs (Level 2) | Fair value option | Municipal bonds |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 377
Significant Other Observable Inputs (Level 2) | Fair value option | Commercial mortgage backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 1,150 | 1,134
Significant Other Observable Inputs (Level 2) | Fair value option | US government and government agencies |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 111 | 110
Significant Other Observable Inputs (Level 2) | Fair value option | Non-US government securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 44,963 | 50,465
Significant Other Observable Inputs (Level 2) | Fair value option | Asset backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 175,790 | 200,163
Significant Other Observable Inputs (Level 2) | Fair value option | Short-term investments |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 107,821 | 43,694
Significant Other Observable Inputs (Level 2) | Fair value option | Equity securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 156 | 641
Significant Other Observable Inputs (Level 2) | Fair value option | Other investments fair value option |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 1,034,251 | 1,296,169
Significant Unobservable Inputs (Level 3) |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 176,927 | 197,799
Liabilities measured at fair value |  | (630) | (7,998)
Significant Unobservable Inputs (Level 3) | Contingent consideration liability |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities measured at fair value |  | (630) | (7,998)
Significant Unobservable Inputs (Level 3) | Securities sold but not yet purchased |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities measured at fair value | [1] | 0 | 0
Significant Unobservable Inputs (Level 3) | Derivative instruments |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities measured at fair value |  | 0 | 0
Significant Unobservable Inputs (Level 3) | Fixed maturities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 3,568 | 14,067
Significant Unobservable Inputs (Level 3) | Fixed maturities | Corporate bonds |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 13 | 8,851
Significant Unobservable Inputs (Level 3) | Fixed maturities | Mortgage backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 208 | 254
Significant Unobservable Inputs (Level 3) | Fixed maturities | Municipal bonds |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 0 | 0
Significant Unobservable Inputs (Level 3) | Fixed maturities | Commercial mortgage backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 0 | 0
Significant Unobservable Inputs (Level 3) | Fixed maturities | US government and government agencies |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 0 | 0
Significant Unobservable Inputs (Level 3) | Fixed maturities | Non-US government securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 0 | 0
Significant Unobservable Inputs (Level 3) | Fixed maturities | Asset backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [2] | 3,347 | 4,962
Significant Unobservable Inputs (Level 3) | Short-term investments |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 0
Significant Unobservable Inputs (Level 3) | Equity securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 42,686 | 55,889
Significant Unobservable Inputs (Level 3) | Derivative instruments |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 0
Significant Unobservable Inputs (Level 3) | Fair value option |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 130,673 | 127,843
Significant Unobservable Inputs (Level 3) | Fair value option | Corporate bonds |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 964 | 932
Significant Unobservable Inputs (Level 3) | Fair value option | Mortgage backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 0
Significant Unobservable Inputs (Level 3) | Fair value option | Municipal bonds |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 0
Significant Unobservable Inputs (Level 3) | Fair value option | Commercial mortgage backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 0
Significant Unobservable Inputs (Level 3) | Fair value option | US government and government agencies |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 0
Significant Unobservable Inputs (Level 3) | Fair value option | Non-US government securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 0
Significant Unobservable Inputs (Level 3) | Fair value option | Asset backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 0
Significant Unobservable Inputs (Level 3) | Fair value option | Short-term investments |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 0
Significant Unobservable Inputs (Level 3) | Fair value option | Equity securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 63,523 | 58,094
Significant Unobservable Inputs (Level 3) | Fair value option | Other investments fair value option |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 66,186 | 68,817
Estimated Fair Value |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 25,936,818 | 22,782,288
Liabilities measured at fair value |  | (107,996) | (114,005)
Estimated Fair Value | Contingent consideration liability |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities measured at fair value |  | (630) | (7,998)
Estimated Fair Value | Securities sold but not yet purchased |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities measured at fair value | [1] | (24,909) | (66,257)
Estimated Fair Value | Derivative instruments |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities measured at fair value |  | (82,457) | (39,750)
Estimated Fair Value | Fixed maturities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 18,515,637 | 17,263,036
Estimated Fair Value | Fixed maturities | Corporate bonds |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 7,965,599 | 6,406,591
Estimated Fair Value | Fixed maturities | Mortgage backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 717,081 | 562,309
Estimated Fair Value | Fixed maturities | Municipal bonds |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 527,410 | 881,926
Estimated Fair Value | Fixed maturities | Commercial mortgage backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 374,360 | 733,108
Estimated Fair Value | Fixed maturities | US government and government agencies |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 4,861,349 | 4,916,592
Estimated Fair Value | Fixed maturities | Non-US government securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 2,302,646 | 2,078,757
Estimated Fair Value | Fixed maturities | Asset backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 1,767,192 | 1,683,753
Estimated Fair Value | Short-term investments |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 2,039,097 | 956,546
Estimated Fair Value | Equity securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 1,502,015 | 850,283
Estimated Fair Value | Derivative instruments |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 130,494 | 48,946
Estimated Fair Value | Fair value option |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 3,749,575 | 3,663,477
Estimated Fair Value | Fair value option | Corporate bonds |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 780,237 | 488,402
Estimated Fair Value | Fair value option | Mortgage backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 13,026 | 11,947
Estimated Fair Value | Fair value option | Municipal bonds |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 0 | 377
Estimated Fair Value | Fair value option | Commercial mortgage backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 1,150 | 1,134
Estimated Fair Value | Fair value option | US government and government agencies |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 4,363 | 1,962
Estimated Fair Value | Fair value option | Non-US government securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 44,963 | 50,465
Estimated Fair Value | Fair value option | Asset backed securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 175,790 | 200,163
Estimated Fair Value | Fair value option | Short-term investments |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 468,704 | 377,014
Estimated Fair Value | Fair value option | Equity securities |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 91,445 | 102,697
Estimated Fair Value | Fair value option | Other investments fair value option |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value |  | 1,152,517 | 1,418,273
Estimated Fair Value | Fair value option | Other investments measured at net asset value |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets measured at fair value | [3] | $ 1,017,380 | $ 1,011,043
[1] | 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.
[2] | 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.”
[3] | 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.

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