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Investment Information - Investment in operating affiliates (Details) € / shares in Units, $ / shares in Units, $ in Thousands, € in Millions | 3 Months Ended | 9 Months Ended | 12 Months Ended |  |
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Sep. 30, 2022 USD ($) | Sep. 30, 2021 USD ($) | Sep. 30, 2022 USD ($) | Sep. 30, 2021 USD ($) | Dec. 31, 2021 USD ($) | Dec. 31, 2021 EUR (€) € / shares | Jul. 01, 2021 $ / shares
Schedule of Equity Method Investments [Line Items] |  |  |  |  |  |  |
Time lag for reporting |  |  | 3 months |  |  |  |
Investment in operating affiliates | $ 891,212 |  | $ 891,212 |  | $ 1,135,655 |  |
Income (loss) from operating affiliates | $ 8,507 | $ 124,119 | $ 37,665 | $ 224,052 |  |  |
Coface |  |  |  |  |  |  |
Schedule of Equity Method Investments [Line Items] |  |  |  |  |  |  |
Percentage ownership | 29.86% |  | 29.86% |  | 29.50% | 29.50% |
Investment in affiliate, price per share | € / shares |  |  |  |  |  | € 9.95 |
Operating affiliate, aggregate cost |  |  |  |  | $ 546,000 | € 453 |
Investment in operating affiliates | $ 506,700 |  | $ 506,700 |  | 630,500 |  |
Operating affiliate, gain on acquisition |  |  |  |  | 74,500 |  |
Greysbridge Holdings Ltd |  |  |  |  |  |  |
Schedule of Equity Method Investments [Line Items] |  |  |  |  |  |  |
Percentage ownership |  |  |  |  |  |  | 40.00%
Investment in affiliate, price per share | $ / shares |  |  |  |  |  |  | $ 35.00
Operating affiliate, aggregate cost |  |  |  |  | 278,900 |  |
Investment in operating affiliates | $ 277,600 |  | $ 277,600 |  | 375,700 |  |
Operating affiliate, gain on acquisition |  |  |  |  | $ 95,700 |  |
Issued Shares Excluding Treasury Stock | Coface |  |  |  |  |  |  |
Schedule of Equity Method Investments [Line Items] |  |  |  |  |  |  |
Percentage ownership | 30.05% |  | 30.05% |  |  |  |
Kelso And Company | Greysbridge Holdings Ltd |  |  |  |  |  |  |
Schedule of Equity Method Investments [Line Items] |  |  |  |  |  |  |
Percentage ownership |  |  |  |  |  |  | 30.00%
Warburg Pincus LLC | Greysbridge Holdings Ltd |  |  |  |  |  |  |
Schedule of Equity Method Investments [Line Items] |  |  |  |  |  |  |
Percentage ownership |  |  |  |  |  |  | 30.00%

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