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, 2024
(dollars in thousands)	Amortized Cost		Gross Unrealized Holding Gains		Gross Unrealized Holding Losses		Estimated Fair Value
Fixed maturity securities:
U.S. Treasury securities	$	4,946,495	$	79,659	$	(31,894)	$	4,994,260
U.S. government-sponsored enterprises	1,420,858		19,757		(65,452)		1,375,163
Obligations of states, municipalities and political subdivisions	4,003,008		36,672		(129,328)		3,910,352
Foreign governments, agencies and supranationals	2,783,826		77,781		(103,644)		2,757,963
Agency mortgage-backed securities	2,738,131		25,754		(86,205)		2,677,680
Non-agency mortgage-backed securities	122,640		—		(3,416)		119,224
Corporate and university bonds	250,785		230		(17,809)		233,206
Total fixed maturity securities	16,265,743		239,853		(437,748)		16,067,848
Short-term investments	2,351,758		4,070		(90)		2,355,738
Investments, available-for-sale	$	18,617,501	$	243,923	$	(437,838)	$	18,423,586


	December 31, 2023
(dollars in thousands)	Amortized Cost		Gross Unrealized Holding Gains		Gross Unrealized Holding Losses		Estimated Fair Value
Fixed maturity securities:
U.S. Treasury securities	$	3,811,293	$	35,824	$	(62,404)	$	3,784,713
U.S. government-sponsored enterprises	1,225,426		7,292		(89,904)		1,142,814
Obligations of states, municipalities and political subdivisions	4,196,096		14,787		(181,578)		4,029,305
Foreign governments, agencies and supranationals	2,554,874		34,352		(142,008)		2,447,218
Agency mortgage-backed securities	2,507,682		8,939		(135,611)		2,381,010
Non-agency mortgage-backed securities	355,673		—		(22,603)		333,070
Corporate and university bonds	281,242		141		(26,781)		254,602
Total fixed maturity securities	14,932,286		101,335		(660,889)		14,372,732
Short-term investments	2,564,620		7,155		(393)		2,571,382
Investments, available-for-sale	$	17,496,906	$	108,490	$	(661,282)	$	16,944,114


	September 30, 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	$	52,587	$	(85)	$	1,420,909	$	(31,809)	$	1,473,496	$	(31,894)
U.S. government-sponsored enterprises	18,881		(584)		723,075		(64,868)		741,956		(65,452)
Obligations of states, municipalities and political subdivisions	153,371		(518)		2,249,754		(128,810)		2,403,125		(129,328)
Foreign governments, agencies and supranationals	16,767		(57)		1,316,288		(103,587)		1,333,055		(103,644)
Agency mortgage-backed securities	53,196		(412)		1,818,419		(85,793)		1,871,615		(86,205)
Non-agency mortgage-backed securities	—		—		119,224		(3,416)		119,224		(3,416)
Corporate and university bonds	2,203		(48)		227,773		(17,761)		229,976		(17,809)
Total fixed maturity securities	297,005		(1,704)		7,875,442		(436,044)		8,172,447		(437,748)
Short-term investments	327,973		(90)		—		—		327,973		(90)
Total	$	624,978	$	(1,794)	$	7,875,442	$	(436,044)	$	8,500,420	$	(437,838)

At September 30, 2024, the Company held 1,079 available-for-sale securities in an unrealized loss position with a total estimated fair value of $8.5 billion and gross unrealized losses of $437.8 million. Of these 1,079 securities, 1,032 securities had been in a continuous unrealized loss position for one year or longer and had a total estimated fair value of $7.9 billion and gross unrealized losses of $436.0 million.


	December 31, 2023
	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	$	317,027	$	(2,147)	$	1,507,784	$	(60,257)	$	1,824,811	$	(62,404)
U.S. government-sponsored enterprises	145,143		(2,134)		723,537		(87,770)		868,680		(89,904)
Obligations of states, municipalities and political subdivisions	679,124		(3,881)		2,332,281		(177,697)		3,011,405		(181,578)
Foreign governments, agencies and supranationals	83,396		(395)		1,492,912		(141,613)		1,576,308		(142,008)
Agency mortgage-backed securities	189,977		(1,871)		1,889,272		(133,740)		2,079,249		(135,611)
Non-agency mortgage-backed securities	—		—		333,070		(22,603)		333,070		(22,603)
Corporate and university bonds	—		—		236,205		(26,781)		236,205		(26,781)
Total fixed maturity securities	1,414,667		(10,428)		8,515,061		(650,461)		9,929,728		(660,889)
Short-term investments	52,601		(393)		—		—		52,601		(393)
Total	$	1,467,268	$	(10,821)	$	8,515,061	$	(650,461)	$	9,982,329	$	(661,282)

At December 31, 2023, the Company held 1,386 available-for-sale securities in an unrealized loss position with a total estimated fair value of $10.0 billion and gross unrealized losses of $661.3 million. Of these 1,386 securities, 1,131 securities had been in a continuous unrealized loss position for one year or longer and had a total estimated fair value of $8.5 billion and gross unrealized losses of $650.5 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, 2024 or December 31, 2023. As of September 30, 2024 or December 31, 2023, 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	$	1,486,434	$	1,478,425
Due after one year through five years	5,577,381		5,559,647
Due after five years through ten years	4,992,655		4,971,587
Due after ten years	1,348,502		1,261,285
	13,404,972		13,270,944
Agency mortgage-backed securities	2,738,131		2,677,680
Non-agency mortgage-backed securities	122,640		119,224
Total fixed maturity securities	$	16,265,743	$	16,067,848


	Quarter Ended September 30,				Nine Months Ended September 30,
(dollars in thousands)	2024		2023		2024		2023
Interest:
Fixed maturity securities	$	131,424	$	98,891	$	372,089	$	269,438
Short-term investments	30,971		26,768		94,809		77,099
Cash and cash equivalents and restricted cash and cash equivalents	41,220		39,473		122,840		102,565
Dividends on equity securities	36,739		31,134		101,263		84,968
	240,354		196,266		691,001		534,070
Investment expenses	(4,877)		(4,059)		(14,194)		(12,835)
Net investment income	$	235,477	$	192,207	$	676,807	$	521,235

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.


	Quarter Ended September 30,				Nine Months Ended September 30,
(dollars in thousands)	2024		2023		2024		2023
Fixed maturity securities, short-term investments and other investments:
Net realized investment gains (losses)	$	13,891	$	(36,093)	$	(4,604)	$	(38,159)
Equity securities:
Change in fair value of securities sold during the period	(6,652)		2,683		(11,263)		16,706
Change in fair value of securities held at the end of the period	910,291		(232,507)		1,705,661		612,626
Total change in fair value	903,639		(229,824)		1,694,398		629,332
Net investment gains (losses)	$	917,530	$	(265,917)	$	1,689,794	$	591,173
Change in net unrealized losses on available-for-sale investments included in other comprehensive income (loss):
Fixed maturity securities	$	546,386	$	(208,598)	$	361,659	$	(167,411)
Short-term investments	4,858		193		(2,782)		(3,195)
Net increase (decrease)	$	551,244	$	(208,405)	$	358,877	$	(170,606)