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Investments
 9 Months Ended
Sep. 30, 2025
Investments, Debt and Equity Securities [Abstract]  
Investments Investments
a) The following tables summarize the Company's available-for-sale investments. Agency mortgage-backed securities include securities issued by U.S. government-sponsored enterprises and U.S. government agencies. The net unrealized holding gains (losses) in the tables below are presented before taxes.

 September 30, 2025
(dollars in thousands)Amortized
Cost		Gross
Unrealized
Holding
Gains		Gross
Unrealized
Holding
Losses		Estimated
Fair
Value
Fixed maturity securities:
U.S. Treasury securities$5,621,479 $61,548 $(17,504)$5,665,523 
U.S. government-sponsored enterprises1,604,245 19,744 (61,921)1,562,068 
Obligations of states, municipalities, and political subdivisions
3,732,612 34,511 (113,294)3,653,829 
Foreign governments, agencies, and supranationals
3,269,118 92,948 (79,566)3,282,500 
Agency mortgage-backed securities
2,866,218 25,412 (67,353)2,824,277 
Non-agency mortgage-backed securities
67,746 2 (703)67,045 
Corporate and university bonds
224,885 164 (20,310)204,739 
Total fixed maturity securities17,386,303 234,329 (360,651)17,259,981 
Short-term investments2,112,271 3,936 (450)2,115,757 
Investments, available-for-sale$19,498,574 $238,265 $(361,101)$19,375,738 

 December 31, 2024
(dollars in thousands)Amortized
Cost		Gross
Unrealized
Holding
Gains		Gross
Unrealized
Holding
Losses		Estimated
Fair
Value
Fixed maturity securities:
U.S. Treasury securities$5,147,365 $8,962 $(68,469)$5,087,858 
U.S. government-sponsored enterprises1,445,171 2,976 (101,911)1,346,236 
Obligations of states, municipalities, and political subdivisions
3,813,146 5,866 (199,520)3,619,492 
Foreign governments, agencies, and supranationals
2,909,561 4,264 (207,302)2,706,523 
Agency mortgage-backed securities
2,771,589 2,096 (123,872)2,649,813 
Non-agency mortgage-backed securities
122,373 — (4,343)118,030 
Corporate and university bonds
248,518 76 (31,007)217,587 
Total fixed maturity securities16,457,723 24,240 (736,424)15,745,539 
Short-term investments2,530,941 548 (6,579)2,524,910 
Investments, available-for-sale$18,988,664 $24,788 $(743,003)$18,270,449 
b) The following tables summarize gross unrealized investment losses on available-for-sale investments by the length of time that securities have continuously been in an unrealized loss position.

September 30, 2025
Less than 12 months12 months or longerTotal
(dollars in thousands)Estimated
Fair
Value		Gross
Unrealized
Holding Losses		Estimated
Fair
Value		Gross
Unrealized
Holding Losses		Estimated
Fair
Value
Gross
Unrealized
Holding
Losses
Fixed maturity securities:
U.S. Treasury securities$382,948 $(954)$1,102,470 $(16,550)$1,485,418 $(17,504)
U.S. government-sponsored enterprises72,182 (493)735,876 (61,428)808,058 (61,921)
Obligations of states, municipalities, and political subdivisions
173,841 (1,119)1,897,264 (112,175)2,071,105 (113,294)
Foreign governments, agencies, and supranationals
227,228 (3,597)1,206,635 (75,969)1,433,863 (79,566)
Agency mortgage-backed securities
122,647 (723)1,442,223 (66,630)1,564,870 (67,353)
Non-agency mortgage-backed securities
— — 61,152 (703)61,152 (703)
Corporate and university bonds
14,429 (254)181,897 (20,056)196,326 (20,310)
Total fixed maturity securities993,275 (7,140)6,627,517 (353,511)7,620,792 (360,651)
Short-term investments392,479 (450)— — 392,479 (450)
Total$1,385,754 $(7,590)$6,627,517 $(353,511)$8,013,271 $(361,101)

At September 30, 2025, the Company held 950 available-for-sale securities in an unrealized loss position with a total estimated fair value of $8.0 billion and gross unrealized losses of $361.1 million. Of these 950 securities, 849 securities had been in a continuous unrealized loss position for one year or longer and had a total estimated fair value of $6.6 billion and gross unrealized losses of $353.5 million.

December 31, 2024
Less than 12 months12 months or longerTotal
(dollars in thousands)Estimated
Fair
Value
Gross
Unrealized
Holding
Losses
Estimated
Fair
Value
Gross
Unrealized
Holding 
Losses
Estimated
Fair
Value
Gross
Unrealized
Holding 
Losses
Fixed maturity securities:
U.S. Treasury securities$1,593,711 $(27,213)$1,444,869 $(41,256)$3,038,580 $(68,469)
U.S. government-sponsored enterprises415,333 (10,938)691,781 (90,973)1,107,114 (101,911)
Obligations of states, municipalities, and political subdivisions
1,133,275 (21,242)2,024,298 (178,278)3,157,573 (199,520)
Foreign governments, agencies, and supranationals
1,056,877 (29,890)1,246,215 (177,412)2,303,092 (207,302)
Agency mortgage-backed securities
757,562 (13,880)1,710,436 (109,992)2,467,998 (123,872)
Non-agency mortgage-backed securities
— — 118,030 (4,343)118,030 (4,343)
Corporate and university bonds
2,107 (137)212,404 (30,870)214,511 (31,007)
Total fixed maturity securities4,958,865 (103,300)7,448,033 (633,124)12,406,898 (736,424)
Short-term investments163,503 (6,579)— — 163,503 (6,579)
Total$5,122,368 $(109,879)$7,448,033 $(633,124)$12,570,401 $(743,003)

At December 31, 2024, the Company held 1,485 available-for-sale securities in an unrealized loss position with a total estimated fair value of $12.6 billion and gross unrealized losses of $743.0 million. Of these 1,485 securities, 966 securities had been in a continuous unrealized loss position for one year or longer and had a total estimated fair value of $7.4 billion and gross unrealized losses of $633.1 million.
The Company completes a detailed analysis each quarter to assess whether the decline in the fair value of any investment below its cost basis is the result of a credit loss. All available-for-sale securities with unrealized losses are reviewed. The Company considers many factors in completing its quarterly review of securities with unrealized losses for credit-related impairment to determine whether a credit loss exists, including the extent to which fair value is below cost, the implied yield to maturity, rating downgrades of the security, and whether or not the issuer has failed to make scheduled principal or interest payments. The Company also takes into consideration information about the financial condition of the issuer and industry factors that could negatively impact the issuer.

If the decline in fair value of an available-for-sale security below its amortized cost is considered to be the result of a credit loss, the Company compares the estimated present value of the cash flows expected to be collected to the amortized cost of the security. The extent to which the estimated present value of the cash flows expected to be collected is less than the amortized cost of the security represents the credit loss, which is recorded as an allowance and recognized in net income. The allowance is limited to the difference between the fair value and the amortized cost of the security. Any remaining decline in fair value represents the non-credit portion of the impairment, which is recognized in other comprehensive income. The Company did not have an allowance for credit losses for any available-for-sale securities as of September 30, 2025 or December 31, 2024. As of September 30, 2025 and December 31, 2024, gross unrealized losses on available-for-sale securities were the result of declines in the fair value of the investments due to increases in interest rates, which are expected to reverse as the securities mature, and foreign currency movements related to available-for-sale securities denominated in a foreign currency.

Quarterly, the Company also considers whether it intends to sell an available-for-sale security or if it is more likely than not that it will be required to sell a security before recovery of its amortized cost. In these instances, a decline in fair value is recognized in net income based on the fair value of the security at the time of assessment, resulting in a new cost basis for the security.

c) The amortized cost and estimated fair value of fixed maturity securities at September 30, 2025 are shown below by contractual maturity.

(dollars in thousands)Amortized
Cost		Estimated
Fair Value
Due in one year or less$1,792,801 $1,791,213 
Due after one year through five years6,637,351 6,670,523 
Due after five years through ten years4,815,043 4,792,723 
Due after ten years1,207,144 1,114,200 
14,452,339 14,368,659 
Mortgage-backed securities
2,933,964 2,891,322 
Total fixed maturity securities$17,386,303 $17,259,981 

d) The following table presents the components of net investment income.

Quarter Ended September 30, Nine Months Ended September 30,
(dollars in thousands)2025202420252024
Interest:
Fixed maturity securities$155,645 $131,424 $444,819 $372,089 
Short-term investments19,406 30,971 58,659 94,809 
Cash and cash equivalents and restricted cash and cash equivalents
37,483 41,220 112,980 122,840 
Dividends on equity securities35,762 36,739 110,769 101,263 
248,296 240,354 727,227 691,001 
Investment expenses(2,621)(4,877)(14,448)(14,194)
Net investment income
$245,675 $235,477 $712,779 $676,807 
e) The following table presents the components of net investment gains included in net income and the change in net unrealized losses included in other comprehensive income. Gross realized investment gains and losses on fixed maturity securities, short-term investments, and other investments were not material to the consolidated financial statements and are presented on a net basis in the following table.

Quarter Ended September 30, Nine Months Ended September 30,
(dollars in thousands)2025202420252024
Fixed maturity securities, short-term investments, and other investments:
Net realized investment gains (losses)$4,695 $13,891 $(13,702)$(4,604)
Equity securities:
Change in fair value of securities sold during the period(1,795)(6,652)1,345 (11,263)
Change in fair value of securities held at the end of the period429,986 910,291 876,395 1,705,661 
Total change in fair value428,191 903,639 877,740 1,694,398 
Net investment gains$432,886 $917,530 $864,038 $1,689,794 
Change in net unrealized losses on available-for-sale investments included in other comprehensive income:
Fixed maturity securities$60,844 $546,386 $585,862 $361,659 
Short-term investments(1,021)4,858 9,517 (2,782)
Net increase$59,823 $551,244 $595,379 $358,877