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.


	March 31, 2025
(dollars in thousands)	Amortized Cost		Gross Unrealized Holding Gains		Gross Unrealized Holding Losses		Estimated Fair Value
Fixed maturity securities:
U.S. Treasury securities	$	5,257,869	$	39,374	$	(33,562)	$	5,263,681
U.S. government-sponsored enterprises	1,495,738		11,133		(77,553)		1,429,318
Obligations of states, municipalities and political subdivisions	3,777,894		15,465		(153,987)		3,639,372
Foreign governments, agencies and supranationals	3,067,330		26,273		(160,800)		2,932,803
Agency mortgage-backed securities	2,776,864		13,005		(90,997)		2,698,872
Non-agency mortgage-backed securities	104,737		—		(2,783)		101,954
Corporate and university bonds	236,169		268		(24,808)		211,629
Total fixed maturity securities	16,716,601		105,518		(544,490)		16,277,629
Short-term investments	2,101,050		371		(2,388)		2,099,033
Investments, available-for-sale	$	18,817,651	$	105,889	$	(546,878)	$	18,376,662


	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 enterprises	1,445,171		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 securities	16,457,723		24,240		(736,424)		15,745,539
Short-term investments	2,530,941		548		(6,579)		2,524,910
Investments, available-for-sale	$	18,988,664	$	24,788	$	(743,003)	$	18,270,449


	March 31, 2025
	Less than 12 months				12 months or longer				Total
(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	$	683,847	$	(4,986)	$	1,277,393	$	(28,576)	$	1,961,240	$	(33,562)
U.S. government-sponsored enterprises	243,333		(3,966)		713,889		(73,587)		957,222		(77,553)
Obligations of states, municipalities and political subdivisions	598,623		(6,410)		2,050,569		(147,577)		2,649,192		(153,987)
Foreign governments, agencies and supranationals	585,664		(11,664)		1,268,147		(149,136)		1,853,811		(160,800)
Agency mortgage-backed securities	162,695		(3,264)		1,631,014		(87,733)		1,793,709		(90,997)
Non-agency mortgage-backed securities	—		—		101,954		(2,783)		101,954		(2,783)
Corporate and university bonds	—		—		202,002		(24,808)		202,002		(24,808)
Total fixed maturity securities	2,274,162		(30,290)		7,244,968		(514,200)		9,519,130		(544,490)
Short-term investments	1,879,046		(2,388)		—		—		1,879,046		(2,388)
Total	$	4,153,208	$	(32,678)	$	7,244,968	$	(514,200)	$	11,398,176	$	(546,878)

At March 31, 2025, the Company held 1,225 available-for-sale securities in an unrealized loss position with a total estimated fair value of $11.4 billion and gross unrealized losses of $546.9 million. Of these 1,225 securities, 932 securities had been in a continuous unrealized loss position for one year or longer and had a total estimated fair value of $7.2 billion and gross unrealized losses of $514.2 million.


	December 31, 2024
	Less than 12 months				12 months or longer				Total
(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 enterprises	415,333		(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 securities	4,958,865		(103,300)		7,448,033		(633,124)		12,406,898		(736,424)
Short-term investments	163,503		(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 March 31, 2025 or December 31, 2024. As of March 31, 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.


(dollars in thousands)	Amortized Cost		Estimated Fair Value
Due in one year or less	$	1,584,937	$	1,568,859
Due after one year through five years	6,422,711		6,349,767
Due after five years through ten years	4,657,827		4,511,211
Due after ten years	1,169,525		1,046,966
	13,835,000		13,476,803
Mortgage-backed securities	2,881,601		2,800,826
Total fixed maturity securities	$	16,716,601	$	16,277,629


	Three Months Ended March 31,
(dollars in thousands)		2025		2024
Interest:
Fixed maturity securities		$	143,345	$	119,476
Short-term investments		19,673		32,184
Cash and cash equivalents and restricted cash and cash equivalents		39,774		39,078
Dividends on equity securities		40,195		32,693
		242,987		223,431
Investment expenses		(5,892)		(5,162)
Net investment income		$	237,095	$	218,269

e) The following table presents the components of net investment gains (losses) included in net income and the change in net unrealized losses included in other comprehensive income (loss). 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.


	Three Months Ended March 31,
(dollars in thousands)		2025		2024
Fixed maturity securities, short-term investments and other investments:
Net realized investment losses		$	(1,801)	$	(4,488)
Equity securities:
Change in fair value of securities sold during the period		(1,322)		43
Change in fair value of securities held at the end of the period		(145,948)		906,726
Total change in fair value		(147,270)		906,769
Net investment gains (losses)		$	(149,071)	$	902,281
Change in net unrealized losses on available-for-sale investments included in other comprehensive income (loss):
Fixed maturity securities		$	273,213	$	(148,487)
Short-term investments		4,014		(7,282)
Net increase (decrease)		$	277,227	$	(155,769)