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Transactions With Related Parties (Details) $ in Thousands | 9 Months Ended | 12 Months Ended |  |
--- | --- | --- | --- | ---
Sep. 30, 2020 USD ($) director | Sep. 30, 2019 USD ($) | Dec. 31, 2017 USD ($) | Jun. 30, 2020 USD ($) | Dec. 31, 2019 USD ($)
Related Party Transaction [Line Items] |  |  |  |  |
Purchases of other investments | $ 841,886 | $ 1,014,925 |  |  |
Reinsurance recoverable on unpaid and paid losses and LAE | $ 4,621,937 |  |  | $ 4,363,507 | $ 4,346,816
Premia Holdings Ltd. |  |  |  |  |
Related Party Transaction [Line Items] |  |  |  |  |
Percentage ownership |  |  | 25.00% |  |
Number of directors appointed by Arch to the Board | director | 2 |  |  |  |
Number of directors on the Board | director | 7 |  |  |  |
Purchases of other investments |  |  | $ 100,000 |  |
Premia Holdings Ltd. | Barbican Group Holdings Limited |  |  |  |  |
Related Party Transaction [Line Items] |  |  |  |  |
Reinsurance recoverable on unpaid and paid losses and LAE | $ 175,800 |  |  |  | 177,700
Funds held liability | $ 150,200 |  |  |  | $ 180,000

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