a) The following tables summarize the Company's available-for-sale investments. Commercial and residential 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, 2023
(dollars in thousands)	Amortized Cost		Gross Unrealized Holding Gains		Gross Unrealized Holding Losses		Estimated Fair Value
Fixed maturity securities:
U.S. Treasury securities	$	3,440,991	$	—	$	(130,162)	$	3,310,829
U.S. government-sponsored enterprises	1,133,417		—		(137,733)		995,684
Obligations of states, municipalities and political subdivisions	4,106,251		879		(308,184)		3,798,946
Foreign governments	1,749,621		2,626		(189,128)		1,563,119
Commercial mortgage-backed securities	2,297,828		11		(208,466)		2,089,373
Residential mortgage-backed securities	511,525		1		(32,686)		478,840
Asset-backed securities	1,226		—		(28)		1,198
Corporate bonds	826,883		758		(114,351)		713,290
Total fixed maturity securities	14,067,742		4,275		(1,120,738)		12,951,279
Short-term investments	2,250,219		3,253		(746)		2,252,726
Investments, available-for-sale	$	16,317,961	$	7,528	$	(1,121,484)	$	15,204,005


	December 31, 2022
(dollars in thousands)	Amortized Cost		Gross Unrealized Holding Gains		Gross Unrealized Holding Losses		Estimated Fair Value
Fixed maturity securities:
U.S. Treasury securities	$	3,050,089	$	2,363	$	(138,493)	$	2,913,959
U.S. government-sponsored enterprises	871,463		154		(106,079)		765,538
Obligations of states, municipalities and political subdivisions	3,973,911		6,503		(247,231)		3,733,183
Foreign governments	1,473,658		2,843		(169,723)		1,306,778
Commercial mortgage-backed securities	2,109,721		395		(169,668)		1,940,448
Residential mortgage-backed securities	553,591		6		(26,804)		526,793
Asset-backed securities	1,693		—		(53)		1,640
Corporate bonds	771,761		836		(104,101)		668,496
Total fixed maturity securities	12,805,887		13,100		(962,152)		11,856,835
Short-term investments	2,663,560		5,760		(58)		2,669,262
Investments, available-for-sale	$	15,469,447	$	18,860	$	(962,210)	$	14,526,097


	September 30, 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	$	1,339,577	$	(33,496)	$	1,971,252	$	(96,666)	$	3,310,829	$	(130,162)
U.S. government-sponsored enterprises	302,362		(13,784)		693,322		(123,949)		995,684		(137,733)
Obligations of states, municipalities and political subdivisions	1,469,105		(36,622)		2,240,788		(271,562)		3,709,893		(308,184)
Foreign governments	442,453		(18,214)		1,095,516		(170,914)		1,537,969		(189,128)
Commercial mortgage-backed securities	321,255		(13,554)		1,764,367		(194,912)		2,085,622		(208,466)
Residential mortgage-backed securities	45,081		(1,074)		433,695		(31,612)		478,776		(32,686)
Asset-backed securities	—		—		1,198		(28)		1,198		(28)
Corporate bonds	98,459		(2,890)		605,598		(111,461)		704,057		(114,351)
Total fixed maturity securities	4,018,292		(119,634)		8,805,736		(1,001,104)		12,824,028		(1,120,738)
Short-term investments	203,710		(746)		—		—		203,710		(746)
Total	$	4,222,002	$	(120,380)	$	8,805,736	$	(1,001,104)	$	13,027,738	$	(1,121,484)

At September 30, 2023, the Company held 1,732 available-for-sale securities in an unrealized loss position with a total estimated fair value of $13.0 billion and gross unrealized losses of $1.1 billion. Of these 1,732 securities, 1,150 securities had been in a continuous unrealized loss position for one year or longer and had a total estimated fair value of $8.8 billion and gross unrealized losses of $1.0 billion.


	December 31, 2022
	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	$	735,605	$	(30,583)	$	1,907,922	$	(107,910)	$	2,643,527	$	(138,493)
U.S. government-sponsored enterprises	413,495		(40,488)		331,391		(65,591)		744,886		(106,079)
Obligations of states, municipalities and political subdivisions	2,474,289		(164,537)		348,943		(82,694)		2,823,232		(247,231)
Foreign governments	900,322		(115,324)		300,423		(54,399)		1,200,745		(169,723)
Commercial mortgage-backed securities	1,611,603		(117,482)		305,217		(52,186)		1,916,820		(169,668)
Residential mortgage-backed securities	516,423		(25,232)		9,342		(1,572)		525,765		(26,804)
Asset-backed securities	1,640		(53)		—		—		1,640		(53)
Corporate bonds	496,766		(74,542)		153,035		(29,559)		649,801		(104,101)
Total fixed maturity securities	7,150,143		(568,241)		3,356,273		(393,911)		10,506,416		(962,152)
Short-term investments	774,480		(58)		—		—		774,480		(58)
Total	$	7,924,623	$	(568,299)	$	3,356,273	$	(393,911)	$	11,280,896	$	(962,210)

At December 31, 2022, the Company held 1,400 available-for-sale securities in an unrealized loss position with a total estimated fair value of $11.3 billion and gross unrealized losses of $962.2 million. Of these 1,400 securities, 246 securities had been in a continuous unrealized loss position for one year or longer and had a total estimated fair value of $3.4 billion and gross unrealized losses of $393.9 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 as of September 30, 2023 or December 31, 2022.

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	$	1,245,195	$	1,221,058
Due after one year through five years	4,731,573		4,490,492
Due after five years through ten years	3,655,839		3,269,429
Due after ten years	1,624,556		1,400,889
	11,257,163		10,381,868
Commercial mortgage-backed securities	2,297,828		2,089,373
Residential mortgage-backed securities	511,525		478,840
Asset-backed securities	1,226		1,198
Total fixed maturity securities	$	14,067,742	$	12,951,279


	Quarter Ended September 30,				Nine Months Ended September 30,
(dollars in thousands)	2023		2022		2023		2022
Interest:
Fixed maturity securities	$	98,891	$	72,477	$	269,438	$	215,541
Short-term investments	26,768		10,316		77,099		14,644
Cash and cash equivalents and restricted cash and cash equivalents	39,473		7,794		102,565		9,619
Dividends on equity securities	31,134		25,962		84,968		74,289
	196,266		116,549		534,070		314,093
Investment expenses	(4,059)		(3,935)		(12,835)		(12,380)
Net investment income	$	192,207	$	112,614	$	521,235	$	301,713

e) The following table presents the components of net investment gains (losses) included in net income (loss) and the change in net unrealized gains (losses) included in other comprehensive 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)	2023		2022		2023		2022
Fixed maturity securities, short-term investments and other investments:
Net realized investment gains (losses)	$	(36,093)	$	2,032	$	(38,159)	$	6,001
Equity securities:
Change in fair value of securities sold during the period	2,683		2,553		16,706		(29,015)
Change in fair value of securities held at the end of the period	(232,507)		(286,068)		612,626		(2,171,511)
Total change in fair value	(229,824)		(283,515)		629,332		(2,200,526)
Net investment gains (losses)	$	(265,917)	$	(281,483)	$	591,173	$	(2,194,525)
Change in net unrealized gains (losses) on available-for-sale investments included in other comprehensive loss:
Fixed maturity securities	$	(208,598)	$	(530,161)	$	(167,411)	$	(1,645,060)
Short-term investments	193		(8,186)		(3,195)		(11,563)
Net decrease	$	(208,405)	$	(538,347)	$	(170,606)	$	(1,656,623)