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Investments - Cost, Gross Unrealized Gains and Losses, and Estimated Fair Value of Trading Investments in Fixed Income Maturities (Details) - USD ($) $ in Millions | Sep. 30, 2024 | Dec. 31, 2023 | Dec. 31, 2022
--- | --- | --- | ---
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost | $ 1,280.5 | $ 1,527.0 | $ 1,576.7
High yield loans |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost | 106.7 | 90.8 | 90.2
Gross Unrealized Gains | 0.6 | 1.3 | 0.2
Gross Unrealized Losses | (0.3) | 0.0 | (2.1)
Fair market value, trading | 107.0 | 92.1 | 88.3
Fixed income securities - trading |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost |  | 1,527.0 | 1,576.7
Gross Unrealized Gains | 12.9 | 4.7 | 0.7
Gross Unrealized Losses | (12.1) | (46.0) | (101.9)
Fair market value, trading |  | 1,485.7 | 1,475.5
Short-term investments |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost |  | 2.1 | 6.3
Gross Unrealized Gains | 0.0 | 0.0 | 0.0
Gross Unrealized Losses | 0.0 | 0.0 | 0.0
Fair market value, trading |  | 2.1 | 6.3
Catastrophe Bonds |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost |  | 1.6 | 5.1
Gross Unrealized Gains | 0.0 | 0.0 | 0.0
Gross Unrealized Losses | 0.0 | 0.0 | (2.2)
Fair market value, trading |  | 1.6 | 2.9
Commercial mortgage loans |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost | 161.4 | 293.2 | 312.6
Gross Unrealized Gains | 0.7 | 1.0 | 0.6
Gross Unrealized Losses | (28.4) | (19.3) | (1.1)
Fair market value, trading | 133.7 | 274.9 | 312.1
Middle market loans |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost | 64.4 | 85.9 | 109.0
Gross Unrealized Gains | 0.1 | 0.0 | 0.0
Gross Unrealized Losses | (0.5) | (1.1) | (2.1)
Fair market value, trading | 64.0 | 84.8 | 106.9
Securities, asset-backed |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost | 129.0 | 83.1 | 68.8
Gross Unrealized Gains | 0.5 | 0.4 | 0.0
Gross Unrealized Losses | (0.3) | (0.6) | (2.0)
Fair market value, trading | 129.2 | 82.9 | 66.8
Global corporates securities |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost | 14.4 | 14.7 | 15.1
Gross Unrealized Gains | 0.0 | 0.0 | 0.0
Gross Unrealized Losses | (0.1) | (0.3) | (0.1)
Fair market value, trading | 14.3 | 14.4 | 15.0
Equity securities — Trading |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost |  |  | 6.6
Gross Unrealized Gains |  |  | 0.0
Gross Unrealized Losses |  |  | 0.0
Fair market value, trading |  |  | 6.6
Short-term investments |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost |  | 18.0 | 25.6
Gross Unrealized Gains |  | 0.0 | 0.0
Gross Unrealized Losses |  | 0.0 | 0.0
Fair market value, trading |  | 18.0 | 25.6
Privately-held investments |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost |  | 494.9 | 537.7
Gross Unrealized Gains | 1.3 | 1.4 | 0.6
Gross Unrealized Losses | (29.3) | (21.3) | (5.3)
Fair market value, trading |  | 475.0 | 533.0
Total - Trading |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost | 1,653.9 | 2,025.6 | 2,125.8
Gross Unrealized Gains | 14.2 | 6.1 | 1.3
Gross Unrealized Losses | (41.4) | (67.3) | (109.4)
Fair market value, trading | 1,626.7 | 1,964.4 | 2,017.7
U.S. government |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost | 262.4 | 248.7 | 267.9
Gross Unrealized Gains | 5.9 | 0.5 | 0.0
Gross Unrealized Losses | (1.2) | (3.7) | (6.3)
Fair market value, trading | 267.1 | 245.5 | 261.6
Municipal |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost | 2.1 | 3.3 | 3.9
Gross Unrealized Gains | 0.0 | 0.0 | 0.0
Gross Unrealized Losses | (0.1) | (0.2) | (0.3)
Fair market value, trading | 2.0 | 3.1 | 3.6
Corporate |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost | 155.0 | 178.8 | 175.3
Gross Unrealized Gains | 1.6 | 0.7 | 0.3
Gross Unrealized Losses | (4.0) | (8.0) | (13.5)
Fair market value, trading | 152.6 | 171.5 | 162.1
Non-U.S government |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost | 24.2 | 35.8 | 32.2
Gross Unrealized Gains | 0.2 | 0.1 | 0.0
Gross Unrealized Losses | (0.2) | (1.1) | (1.8)
Fair market value, trading | 24.2 | 34.8 | 30.4
Asset-backed |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost | 688.5 | 936.0 | 970.3
Gross Unrealized Gains | 4.1 | 2.1 | 0.2
Gross Unrealized Losses | (3.9) | (29.9) | (74.0)
Fair market value, trading | 688.7 | 908.2 | 896.5
Agency mortgage-backed |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost | 35.2 | 25.0 | 24.7
Gross Unrealized Gains | 0.5 | 0.0 | 0.0
Gross Unrealized Losses | (2.3) | (2.8) | (3.3)
Fair market value, trading | 33.4 | 22.2 | 21.4
Non-U.S. government-backed corporate |  |  |
Schedule of Trading Securities and Other Trading Items [Line Items] |  |  |
Debt Securities, Trading, Amortized Cost | 6.4 | 8.6 | 12.2
Gross Unrealized Gains | 0.0 | 0.0 | 0.0
Gross Unrealized Losses | (0.1) | (0.3) | (0.6)
Fair market value, trading | $ 6.3 | $ 8.3 | $ 11.6

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