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Reinsurance - Effects of reinsurance (Details) - USD ($) $ in Thousands | 12 Months Ended
--- | ---
Dec. 31, 2022 | Dec. 31, 2021 | Dec. 31, 2020
Premiums Written |  |  |
Direct | $ 8,540,787 | $ 7,706,832 | $ 6,553,910
Assumed | 6,785,660 | 5,045,655 | 3,534,158
Ceded | (4,249,258) | (3,734,150) | (2,650,352)
Net premiums written | 11,077,189 | 9,018,337 | 7,437,716
Premiums Earned |  |  |
Direct | 8,057,635 | 7,149,794 | 6,361,451
Assumed | 5,767,738 | 4,333,873 | 3,213,873
Ceded | (4,147,296) | (3,401,369) | (2,583,389)
Net premiums earned | 9,678,077 | 8,082,298 | 6,991,935
Losses and Loss Adjustment Expenses |  |  |
Direct | 3,990,768 | 4,266,758 | 4,392,392
Assumed | 3,559,133 | 2,826,820 | 2,204,323
Ceded | (2,522,384) | (2,508,775) | (1,907,116)
Net | $ 5,027,517 | $ 4,584,803 | $ 4,689,599

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