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Fair Value Measurements - Inputs Used (Details) $ in Millions | 6 Months Ended | 12 Months Ended
--- | --- | ---
Jun. 30, 2023 USD ($) | Jun. 30, 2022 USD ($) | Dec. 31, 2022 USD ($) | Dec. 31, 2021 USD ($) | Dec. 31, 2020 USD ($)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Gross written premiums | $ 2,125.2 | $ 2,351.3 | $ 4,338.7 | $ 3,938.4 | $ 3,698.5
Held for trading financial assets, at fair value | Recurring |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Privately-held Investments, at fair value | 482.4 |  | 533.0 | 307.1 |
Held for trading financial assets, at fair value | Recurring | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Privately-held Investments, at fair value | $ 482.4 |  | $ 533.0 | $ 307.1 |
Discounted cash flow | Commercial mortgage loans | Minimum | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Measurement inputs | 0.037 |  | 0.039 |  |
Discounted cash flow | Commercial mortgage loans | Maximum | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Measurement inputs | 0.112 |  | 0.094 |  |
Discounted cash flow | Commercial mortgage loans | Weighted Average | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Measurement inputs | 0.062 |  | 0.053 |  |
Discounted cash flow | Commercial mortgage loans | Recurring | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Privately-held Investments, at fair value | $ 270.0 |  | $ 200.7 |  |
Discounted cash flow | Middle market loans | Minimum | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Measurement inputs | 0.058 |  | 0.074 |  |
Discounted cash flow | Middle market loans | Maximum | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Measurement inputs | 0.093 |  | 0.185 |  |
Discounted cash flow | Middle market loans | Weighted Average | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Measurement inputs | 0.068 |  | 0.099 |  |
Discounted cash flow | Middle market loans | Recurring | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Privately-held Investments, at fair value | $ 58.4 |  | $ 106.9 |  |
Discounted cash flow | Asset-backed | Minimum | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Measurement inputs | 0.064 |  | 0.058 |  |
Discounted cash flow | Asset-backed | Maximum | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Measurement inputs | 0.074 |  | 0.093 |  |
Discounted cash flow | Asset-backed | Weighted Average | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Measurement inputs | 0.064 |  | 0.067 |  |
Discounted cash flow | Asset-backed | Recurring | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Privately-held Investments, at fair value | $ 14.8 |  |  |  |
Discounted cash flow | Global corporate securities | Minimum | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Measurement inputs | 0.086 |  | 0.064 |  |
Discounted cash flow | Global corporate securities | Maximum | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Measurement inputs | 0.086 |  | 0.064 |  |
Discounted cash flow | Global corporate securities | Weighted Average | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Measurement inputs | 0.086 |  | 0.064 |  |
Discounted cash flow | Global corporate securities | Recurring | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Privately-held Investments, at fair value | $ 12.1 |  | $ 15.0 |  |
Discounted cash flow | Short-term investments | Recurring | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Privately-held Investments, at fair value | 482.4 |  |  |  |
Transaction value | Commercial mortgage loans | Recurring | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Privately-held Investments, at fair value | $ 25.0 |  | 85.8 |  |
Liquidation method | Commercial mortgage loans | Minimum | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Measurement inputs | 0.076 |  |  |  |
Liquidation method | Commercial mortgage loans | Maximum | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Measurement inputs | 0.209 |  |  |  |
Liquidation method | Commercial mortgage loans | Weighted Average | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Measurement inputs | 0.108 |  |  |  |
Liquidation method | Commercial mortgage loans | Recurring | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Privately-held Investments, at fair value |  |  | 25.6 |  |
Recovery approach | Commercial mortgage loans | Recurring | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Privately-held Investments, at fair value | $ 102.1 |  |  |  |
Recovery approach | Asset-backed | Recurring | Level 3 |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |  |  |
Privately-held Investments, at fair value |  |  | $ 66.8 |  |

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