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.


	June 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	$	3,262,114	$	280	$	(133,542)	$	3,128,852
U.S. government-sponsored enterprises	1,044,843		104		(106,212)		938,735
Obligations of states, municipalities and political subdivisions	4,093,715		2,728		(220,108)		3,876,335
Foreign governments	1,691,459		3,717		(151,550)		1,543,626
Commercial mortgage-backed securities	2,251,522		291		(178,257)		2,073,556
Residential mortgage-backed securities	508,692		3		(28,773)		479,922
Asset-backed securities	1,241		—		(37)		1,204
Corporate bonds	799,971		811		(97,320)		703,462
Total fixed maturity securities	13,653,557		7,934		(915,799)		12,745,692
Short-term investments	2,036,747		3,840		(1,526)		2,039,061
Investments, available-for-sale	$	15,690,304	$	11,774	$	(917,325)	$	14,784,753


	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


	June 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	$	1,072,516	$	(17,213)	$	1,956,782	$	(116,329)	$	3,029,298	$	(133,542)
U.S. government-sponsored enterprises	301,249		(6,205)		628,588		(100,007)		929,837		(106,212)
Obligations of states, municipalities and political subdivisions	1,434,351		(18,517)		1,929,349		(201,591)		3,363,700		(220,108)
Foreign governments	359,569		(12,927)		1,005,886		(138,623)		1,365,455		(151,550)
Commercial mortgage-backed securities	419,295		(12,357)		1,634,450		(165,900)		2,053,745		(178,257)
Residential mortgage-backed securities	115,044		(2,216)		364,356		(26,557)		479,400		(28,773)
Asset-backed securities	—		—		1,204		(37)		1,204		(37)
Corporate bonds	90,952		(1,540)		591,258		(95,780)		682,210		(97,320)
Total fixed maturity securities	3,792,976		(70,975)		8,111,873		(844,824)		11,904,849		(915,799)
Short-term investments	1,324,927		(1,526)		—		—		1,324,927		(1,526)
Total	$	5,117,903	$	(72,501)	$	8,111,873	$	(844,824)	$	13,229,776	$	(917,325)

At June 30, 2023, the Company held 1,603 available-for-sale securities in an unrealized loss position with a total estimated fair value of $13.2 billion and gross unrealized losses of $917.3 million. Of these 1,603 securities, 991 securities had been in a continuous unrealized loss position for one year or longer and had a total estimated fair value of $8.1 billion and gross unrealized losses of $844.8 million.


	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 June 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. As of June 30, 2023, the Company did not intend to sell or believe it would be required to sell any available-for-sale securities in an unrealized loss position before recovery of their amortized cost.


(dollars in thousands)	Amortized Cost		Estimated Fair Value
Due in one year or less	$	1,193,540	$	1,170,094
Due after one year through five years	4,544,954		4,325,414
Due after five years through ten years	3,382,145		3,077,695
Due after ten years	1,771,463		1,617,807
	10,892,102		10,191,010
Commercial mortgage-backed securities	2,251,522		2,073,556
Residential mortgage-backed securities	508,692		479,922
Asset-backed securities	1,241		1,204
Total fixed maturity securities	$	13,653,557	$	12,745,692


	Quarter Ended June 30,				Six Months Ended June 30,
(dollars in thousands)	2023		2022		2023		2022
Interest:
Fixed maturity securities	$	88,419	$	71,920	$	170,547	$	143,064
Short-term investments	23,712		3,354		50,331		4,328
Cash and cash equivalents	35,491		2,023		63,092		1,825
Dividends on equity securities	26,352		23,590		53,834		48,327
	173,974		100,887		337,804		197,544
Investment expenses	(4,281)		(4,092)		(8,776)		(8,445)
Net investment income	$	169,693	$	96,795	$	329,028	$	189,099

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 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 June 30,				Six Months Ended June 30,
(dollars in thousands)	2023		2022		2023		2022
Fixed maturity securities, short-term investments and other investments:
Net realized investment gains (losses)	$	1,155	$	(2,259)	$	(2,066)	$	3,969
Equity securities:
Change in fair value of securities sold during the period	2,434		(2,113)		13,487		(19,231)
Change in fair value of securities held at the end of the period	480,938		(1,550,271)		845,669		(1,897,780)
Total change in fair value	483,372		(1,552,384)		859,156		(1,917,011)
Net investment gains (losses)	$	484,527	$	(1,554,643)	$	857,090	$	(1,913,042)
Change in net unrealized gains (losses) on available-for-sale investments included in other comprehensive income (loss):
Fixed maturity securities	$	(167,992)	$	(449,089)	$	41,187	$	(1,114,899)
Short-term investments	(2,578)		(9,239)		(3,388)		(3,377)
Net increase (decrease)	$	(170,570)	$	(458,328)	$	37,799	$	(1,118,276)