Reserves For Losses And Loss Expenses (Tables)

12 Months Ended

Dec. 31, 2020

Insurance [Abstract]

Loss and loss expenses incurred, net of reinsurance, and cumulative paid claims and claim adjustment expenses, net of reinsurance

Insurance

Other Liability

(In thousands)

Loss and Loss Expenses Incurred, Net of Reinsurance																					As of December 31, 2020
For the Year Ended December 31,
	Unaudited
Accident Year	2011		2012		2013		2014		2015		2016		2017		2018		2019		2020		IBNR		Cumulative Number of Reported Claims
2011	$	665,626	$	671,712	$	657,819	$	657,143	$	652,134	$	647,241	$	643,358	$	632,565	$	643,446	$	644,565	$	16,298	24
2012	—		692,549		701,212		702,022		708,805		712,698		722,946		717,453		715,466		713,714		23,827		24
2013	—		—		750,993		791,768		784,674		784,487		805,447		811,775		806,348		810,500		41,398		26
2014	—		—		—		848,658		851,404		849,440		853,826		866,096		872,150		867,239		66,901		27
2015	—		—		—		—		953,198		988,569		963,451		966,872		968,783		979,014		99,480		27
2016	—		—		—		—		—		1,019,851		1,012,851		1,021,524		1,032,780		1,046,823		171,325		27
2017	—		—		—		—		—		—		1,067,556		1,101,376		1,123,930		1,140,639		253,192		27
2018	—		—		—		—		—		—		—		1,106,108		1,133,601		1,123,121		408,131		26
2019	—		—		—		—		—		—		—		—		1,243,287		1,240,028		662,084		25
2020	—		—		—		—		—		—		—		—		—		1,342,065		1,099,126		17
Total																			$	9,907,708

Cumulative Paid Claims and Claim Adjustment Expenses, Net of Reinsurance
For the Year Ended December 31,
	Unaudited
Accident Year	2011		2012		2013		2014		2015		2016		2017		2018		2019		2020
2011	$	48,846	$	141,216	$	265,109	$	377,836	$	469,123	$	522,488	$	554,278	$	573,364	$	592,637	$	604,657
2012	—		57,599		157,499		298,644		416,561		512,283		579,454		621,454		652,178		667,749
2013	—		—		63,358		188,411		331,779		472,731		588,650		649,657		695,301		721,879
2014	—		—		—		79,111		191,320		339,194		481,706		595,794		681,976		732,313
2015	—		—		—		—		82,817		211,212		382,869		539,242		677,386		758,890
2016	—		—		—		—		—		69,579		209,217		390,664		559,218		678,209
2017	—		—		—		—		—		—		80,163		256,345		453,973		639,977
2018	—		—		—		—		—		—		—		86,958		264,629		436,282
2019	—		—		—		—		—		—		—		—		88,422		275,803
2020	—		—		—		—		—		—		—		—		—		72,274
Total																			$	5,588,033
	Reserves for loss and loss adjustment expenses before 2011, net of reinsurance																		117,290
	Reserves for loss and loss adjustment expenses, net of reinsurance																		$	4,436,965

Workers' Compensation

(In thousands)

Loss and Loss Expenses Incurred, Net of Reinsurance																					As of December 31, 2020
For the Year Ended December 31,
	Unaudited
Accident Year	2011		2012		2013		2014		2015		2016		2017		2018		2019		2020		IBNR		Cumulative Number of Reported Claims
2011	$	413,429	$	444,887	$	457,134	$	470,026	$	472,087	$	474,076	$	475,729	$	471,471	$	473,766	$	472,593	$	14,609	46
2012	—		501,681		501,810		503,956		503,863		509,167		512,707		508,169		506,730		506,827		19,328		48
2013	—		—		552,570		547,295		546,995		543,238		547,000		542,274		541,926		540,322		23,485		53
2014	—		—		—		639,436		637,307		627,767		617,242		615,435		604,030		600,194		36,001		57
2015	—		—		—		—		712,800		690,525		650,997		641,169		626,432		620,741		50,083		58
2016	—		—		—		—		—		702,716		696,339		684,700		660,520		651,278		51,369		58
2017	—		—		—		—		—		—		762,093		733,505		689,622		673,216		64,176		58
2018	—		—		—		—		—		—		—		778,964		724,697		715,055		80,252		56
2019	—		—		—		—		—		—		—		—		784,281		721,018		141,657		53
2020	—		—		—		—		—		—		—		—		—		725,245		319,131		39
Total																			$	6,226,489

Cumulative Paid Claims and Claim Adjustment Expenses, Net of Reinsurance
For the Year Ended December 31,
	Unaudited
Accident Year	2011		2012		2013		2014		2015		2016		2017		2018		2019		2020
2011	$	106,899	$	236,207	$	309,509	$	355,909	$	385,759	$	408,304	$	420,945	$	428,811	$	436,905	$	442,163
2012	—		115,536		255,063		339,560		387,368		419,588		437,196		451,991		459,119		466,028
2013	—		—		117,900		277,538		363,028		414,160		447,894		466,580		479,104		489,075
2014	—		—		—		148,405		319,743		412,611		471,235		503,915		521,141		531,475
2015	—		—		—		—		139,320		323,744		421,734		477,541		512,933		531,512
2016	—		—		—		—		—		142,998		338,835		446,072		504,850		537,861
2017	—		—		—		—		—		—		153,456		362,299		468,817		525,753
2018	—		—		—		—		—		—		—		171,006		397,464		508,546
2019	—		—		—		—		—		—		—		—		184,715		397,376
2020	—		—		—		—		—		—		—		—		—		172,478
Total																			$	4,602,267
			Reserves for loss and loss adjustment expenses before 2011, net of reinsurance																219,529
			Reserves for loss and loss adjustment expenses, net of reinsurance																$	1,843,751

Professional Liability

(In thousands)

Loss and Loss Expenses Incurred, Net of Reinsurance																					As of December 31, 2020
For the Year Ended December 31,
	Unaudited
Accident Year	2011		2012		2013		2014		2015		2016		2017		2018		2019		2020		IBNR		Cumulative Number of Reported Claims
2011	$	180,508	$	165,844	$	187,797	$	190,849	$	177,748	$	174,038	$	177,335	$	176,396	$	176,944	$	181,874	$	5,325	4
2012	—		242,530		245,962		268,761		253,146		241,342		247,789		246,478		247,072		249,846		5,919		6
2013	—		—		275,051		251,419		245,984		252,024		273,679		282,150		287,310		284,837		10,867		6
2014	—		—		—		257,442		250,025		263,540		246,983		242,449		261,150		259,892		19,573		7
2015	—		—		—		—		262,459		261,069		278,012		278,868		294,435		285,557		29,712		8
2016	—		—		—		—		—		313,365		327,706		364,312		405,390		442,521		49,740		9
2017	—		—		—		—		—		—		335,565		334,682		340,569		379,408		85,159		10
2018	—		—		—		—		—		—		—		337,865		324,934		335,852		125,091		10
2019	—		—		—		—		—		—		—		—		339,825		336,559		176,941		11
2020	—		—		—		—		—		—		—		—		—		398,429		328,303		10
Total																			$	3,154,775

Cumulative Paid Claims and Claim Adjustment Expenses, Net of Reinsurance
For the Year Ended December 31,
	Unaudited
Accident Year	2011		2012		2013		2014		2015		2016		2017		2018		2019		2020
2011	$	18,803	$	62,560	$	103,263	$	134,862	$	151,135	$	159,309	$	167,595	$	169,191	$	170,873	$	172,294
2012	—		22,269		87,951		129,282		160,243		191,702		216,199		225,442		233,637		236,481
2013	—		—		24,893		64,439		120,224		178,579		208,368		250,507		260,023		265,297
2014	—		—		—		19,773		84,457		139,934		177,575		201,002		218,055		229,615
2015	—		—		—		—		20,565		85,945		140,517		188,608		217,625		234,585
2016	—		—		—		—		—		28,833		103,321		202,906		257,221		299,813
2017	—		—		—		—		—		—		36,839		97,034		163,731		244,396
2018	—		—		—		—		—		—		—		28,432		100,284		156,102
2019	—		—		—		—		—		—		—		—		32,081		98,625
2020	—		—		—		—		—		—		—		—		—		28,474
Total																			$	1,965,682
	Reserves for loss and loss adjustment expenses before 2011, net of reinsurance																		14,011
	Reserves for loss and loss adjustment expenses, net of reinsurance																		$	1,203,104

Commercial Automobile

(In thousands)

Loss and Loss Expenses Incurred, Net of Reinsurance																					As of December 31, 2020
For the Year Ended December 31,
	Unaudited
Accident Year	2011		2012		2013		2014		2015		2016		2017		2018		2019		2020		IBNR		Cumulative Number of Reported Claims
2011	$	314,028	$	322,516	$	329,917	$	334,816	$	343,421	$	344,174	$	345,044	$	346,619	$	346,490	$	342,581	$	100	37
2012	—		314,309		326,831		342,588		355,609		364,717		364,966		367,216		366,493		366,649		365		41
2013	—		—		327,514		349,136		368,894		377,696		368,106		367,720		366,885		365,820		586		44
2014	—		—		—		363,996		385,329		420,139		418,150		415,727		415,621		411,158		1,506		47
2015	—		—		—		—		390,002		419,663		425,865		434,254		435,438		433,888		3,111		53
2016	—		—		—		—		—		434,582		434,117		445,516		446,521		443,338		8,135		52
2017	—		—		—		—		—		—		431,504		429,372		431,177		435,099		14,298		47
2018	—		—		—		—		—		—		—		443,045		463,057		479,502		29,712		45
2019	—		—		—		—		—		—		—		—		483,483		488,777		74,684		44
2020	—		—		—		—		—		—		—		—		—		523,753		264,630		28
Total																			$	4,290,565

Cumulative Paid Claims and Claim Adjustment Expenses, Net of Reinsurance
For the Year Ended December 31,
	Unaudited
Accident Year	2011		2012		2013		2014		2015		2016		2017		2018		2019		2020
2011	$	135,350	$	211,756	$	262,685	$	296,370	$	321,814	$	333,987	$	338,325	$	340,360	$	340,799	$	341,781
2012	—		136,844		215,214		273,446		312,342		344,952		356,264		361,342		362,426		363,587
2013	—		—		142,929		218,596		267,253		323,227		344,357		354,280		363,038		363,805
2014	—		—		—		155,614		237,765		329,979		367,283		396,089		404,087		406,795
2015	—		—		—		—		160,237		267,420		327,462		372,587		400,304		413,838
2016	—		—		—		—		—		186,867		282,375		344,503		393,509		412,967
2017	—		—		—		—		—		—		181,317		268,201		327,765		372,689
2018	—		—		—		—		—		—		—		180,306		281,888		350,572
2019	—		—		—		—		—		—		—		—		185,488		290,449
2020	—		—		—		—		—		—		—		—		—		142,826
Total																			$	3,459,309
			Reserves for loss and loss adjustment expenses before 2011, net of reinsurance																4,119
			Reserves for loss and loss adjustment expenses, net of reinsurance																$	835,375

Short-tail lines

(In thousands)

Loss and Loss Expenses Incurred, Net of Reinsurance																					As of December 31, 2020
For the Year Ended December 31,
	Unaudited
Accident Year	2011		2012		2013		2014		2015		2016		2017		2018		2019		2020		IBNR		Cumulative Number of Reported Claims
2011	$	494,704	$	490,235	$	472,041	$	467,989	$	467,205	$	461,629	$	459,369	$	459,557	$	463,053	$	456,106	$	550	22
2012	—		532,843		540,714		542,017		537,142		508,366		507,344		509,216		508,294		509,058		2,406		24
2013	—		—		580,902		591,686		582,666		555,715		554,167		550,604		548,672		547,932		2,160		25
2014	—		—		—		714,360		719,508		667,627		666,246		667,061		667,278		669,729		2,930		30
2015	—		—		—		—		747,683		734,204		730,251		728,720		720,324		718,820		8,958		32
2016	—		—		—		—		—		775,477		778,376		765,311		759,735		754,184		9,360		34
2017	—		—		—		—		—		—		754,135		754,217		748,399		747,739		12,056		42
2018	—		—		—		—		—		—		—		761,177		750,123		747,396		23,631		48
2019	—		—		—		—		—		—		—		—		722,122		702,281		43,842		43
2020	—		—		—		—		—		—		—		—		—		901,698		244,828		34
Total																			$	6,754,943

Cumulative Paid Claims and Claim Adjustment Expenses, Net of Reinsurance
For the Year Ended December 31,
	Unaudited
Accident Year	2011		2012		2013		2014		2015		2016		2017		2018		2019		2020
2011	$	303,049	$	417,792	$	436,787	$	441,025	$	445,323	$	447,016	$	447,619	$	450,432	$	454,991	$	455,702
2012	—		282,703		456,872		508,333		519,093		499,014		500,181		504,451		505,183		506,308
2013	—		—		315,304		491,801		541,563		533,269		540,132		541,400		541,990		543,195
2014	—		—		—		374,757		604,942		615,833		635,415		650,762		658,053		660,640
2015	—		—		—		—		397,261		613,868		669,706		691,705		701,503		707,349
2016	—		—		—		—		—		417,988		672,013		713,634		729,011		734,110
2017	—		—		—		—		—		—		445,835		690,343		719,286		731,440
2018	—		—		—		—		—		—		—		415,529		662,657		709,202
2019	—		—		—		—		—		—		—		—		405,500		616,695
2020	—		—		—		—		—		—		—		—		—		460,656
Total																			$	6,125,297
	Reserves for loss and loss adjustment expenses before 2011, net of reinsurance																		1,571
	Reserves for loss and loss adjustment expenses, net of reinsurance																		$	631,217

Reinsurance & Monoline Excess

Casualty

(In thousands)

Loss and Loss Expenses Incurred, Net of Reinsurance																					As of December 31, 2020
For the Year Ended December 31,
	Unaudited
Accident Year	2011		2012		2013		2014		2015		2016		2017		2018		2019		2020		IBNR
2011	$	293,274	$	312,321	$	306,721	$	301,847	$	309,235	$	307,772	$	299,076	$	295,376	$	301,670	$	298,292	$	13,368
2012	—		335,187		339,236		334,299		326,934		337,777		340,026		337,901		334,461		337,437		14,927
2013	—		—		322,718		273,683		276,688		288,556		297,121		302,768		307,426		305,080		21,094
2014	—		—		—		323,837		323,920		323,130		334,617		328,741		328,289		339,941		25,778
2015	—		—		—		—		262,448		234,862		233,443		255,400		296,297		306,296		35,570
2016	—		—		—		—		—		243,970		256,011		248,367		270,833		304,845		45,117
2017	—		—		—		—		—		—		234,561		224,835		242,603		265,111		58,308
2018	—		—		—		—		—		—		—		224,640		213,665		234,286		88,934
2019	—		—		—		—		—		—		—		—		240,408		234,813		142,399
2020	—		—		—		—		—		—		—		—		—		305,114		255,936
Total																			$	2,931,215

Cumulative Paid Claims and Claim Adjustment Expenses, Net of Reinsurance
For the Year Ended December 31,
	Unaudited
Accident Year	2011		2012		2013		2014		2015		2016		2017		2018		2019		2020
2011	$	17,976	$	52,597	$	98,086	$	134,814	$	170,629	$	194,320	$	210,245	$	222,618	$	234,552	$	246,140
2012	—		22,516		62,563		112,474		153,950		188,955		221,679		243,586		259,429		279,123
2013	—		—		29,122		64,239		111,189		145,508		179,494		207,312		227,884		244,082
2014	—		—		—		21,441		69,568		116,908		156,495		199,846		229,562		254,532
2015	—		—		—		—		17,952		48,833		91,949		142,334		179,884		206,864
2016	—		—		—		—		—		19,998		62,094		100,862		141,301		172,994
2017	—		—		—		—		—		—		16,498		40,440		70,129		124,641
2018	—		—		—		—		—		—		—		11,187		41,382		78,219
2019	—		—		—		—		—		—		—		—		14,641		39,435
2020	—		—		—		—		—		—		—		—		—		20,845
Total																			$	1,666,875
	Reserves for loss and loss adjustment expenses before 2011, net of reinsurance																		380,546
			Reserves for loss and loss adjustment expenses, net of reinsurance																$	1,644,886

Monoline Excess

(In thousands)

Loss and Loss Expenses Incurred, Net of Reinsurance																					As of December 31, 2020
For the Year Ended December 31,
	Unaudited
Accident Year	2011		2012		2013		2014		2015		2016		2017		2018		2019		2020		IBNR
2011	$	88,650	$	93,993	$	98,051	$	89,031	$	87,030	$	83,850	$	78,246	$	74,109	$	72,091	$	69,205	$	10,955
2012	—		72,366		73,230		73,670		75,274		72,441		67,878		69,361		67,205		66,269		9,184
2013	—		—		63,995		50,355		48,143		42,419		38,551		35,120		31,752		29,758		11,097
2014	—		—		—		63,561		57,650		49,478		45,758		41,671		42,541		42,618		15,319
2015	—		—		—		—		69,977		57,897		50,099		45,115		39,682		39,781		17,184
2016	—		—		—		—		—		72,657		70,281		71,404		64,957		65,485		20,435
2017	—		—		—		—		—		—		76,701		80,508		70,749		71,025		27,947
2018	—		—		—		—		—		—		—		77,820		72,505		71,448		34,366
2019	—		—		—		—		—		—		—				78,929		77,482		39,832
2020	—		—		—		—		—		—		—		—		—		84,354		59,854
Total																			$	617,425

Cumulative Paid Claims and Claim Adjustment Expenses, Net of Reinsurance
For the Year Ended December 31,
	Unaudited
Accident Year	2011		2012		2013		2014		2015		2016		2017		2018		2019		2020
2011	$	2,593	$	4,848	$	6,395	$	14,042	$	15,684	$	18,638	$	20,164	$	21,463	$	23,686	$	24,842
2012	—		1,127		6,097		10,815		11,167		13,234		15,738		17,982		20,004		22,528
2013	—		—		647		1,897		2,158		3,008		3,396		4,418		5,349		6,476
2014	—		—		—		377		1,729		3,354		4,175		5,808		7,595		11,154
2015	—		—		—		—		2,069		2,481		3,272		4,099		4,416		5,083
2016	—		—		—		—		—		2,498		4,783		5,573		5,928		7,685
2017	—		—		—		—		—		—		6,282		12,810		15,356		17,327
2018	—		—		—		—		—		—		—		6,141		8,230		9,368
2019	—		—		—		—		—		—		—		—		6,241		10,884
2020	—		—		—		—		—		—		—		—		—		4,869
Total																			$	120,216
	Reserves for loss and loss adjustment expenses before 2011, net of reinsurance																		735,818
	Reserves for loss and loss adjustment expenses, net of reinsurance																		$	1,233,027

Property

(In thousands)

Loss and Loss Expenses Incurred, Net of Reinsurance																					As of December 31, 2020
For the Year Ended December 31,
	Unaudited
Accident Year	2011		2012		2013		2014		2015		2016		2017		2018		2019		2020		IBNR
2011	$	95,737	$	88,345	$	85,462	$	86,879	$	85,304	$	85,028	$	84,744	$	85,160	$	84,938	$	84,112	$	366
2012	—		104,336		95,164		86,809		85,846		84,285		84,286		85,222		85,025		91,342		1,429
2013	—		—		142,340		113,201		114,638		112,419		113,053		112,373		110,165		108,017		1,757
2014	—		—		—		113,962		97,411		97,933		100,640		99,892		99,535		99,924		2,185
2015	—		—		—		—		127,852		118,026		132,399		130,888		130,005		131,669		2,404
2016	—		—		—		—		—		168,634		174,935		182,171		181,429		186,786		4,318
2017	—		—		—		—		—		—		207,096		200,917		199,892		198,529		8,040
2018	—		—		—		—		—		—		—		108,829		112,503		103,751		2,423
2019	—		—		—		—		—		—		—		—		103,749		77,618		6,913
2020	—		—		—		—		—		—		—		—		—		115,116		48,509
Total																			$	1,196,864

Cumulative Paid Claims and Claim Adjustment Expenses, Net of Reinsurance
For the Year Ended December 31,
	Unaudited
Accident Year	2011		2012		2013		2014		2015		2016		2017		2018		2019		2020
2011	$	31,545	$	59,054	$	73,601	$	76,267	$	78,835	$	82,038	$	82,587	$	83,669	$	83,750	$	83,229
2012	—		15,725		51,964		64,489		70,955		77,842		79,407		82,129		83,007		89,194
2013	—		—		36,668		74,806		92,968		101,947		104,756		106,483		108,062		104,863
2014	—		—		—		39,019		67,251		82,646		88,857		92,011		93,723		95,222
2015	—		—		—		—		53,482		89,366		109,378		118,977		123,023		125,939
2016	—		—		—		—		—		78,994		133,805		157,834		169,013		176,509
2017	—		—		—		—		—		—		72,180		141,651		172,100		180,242
2018	—		—		—		—		—		—		—		34,195		65,527		82,815
2019	—		—		—		—		—		—		—		—		23,103		54,864
2020	—		—		—		—		—		—		—		—		—		26,637
Total																			$	1,019,514
	Reserves for loss and loss adjustment expenses before 2011, net of reinsurance																		1,928
	Reserves for loss and loss adjustment expenses, net of reinsurance																		$	179,278

Reconciliation of net incurred and paid claims development to reserves for loss and loss adjustment expenses

The reconciliation of the net incurred and paid claims development tables to the reserves for losses and loss expenses in the consolidated balance sheet is as follows:

(In thousands)		December 31, 2020
Undiscounted reserves for loss and loss expenses, net of reinsurance:
	Other liability	$	4,436,965
	Workers' compensation	1,843,751
	Professional liability	1,203,104
	Commercial automobile	835,375
	Short-tail lines	631,217
	Other	96,257
	Insurance	9,046,669
	Casualty	1,644,886
	Monoline excess	1,233,027
	Property	179,278
	Reinsurance & Monoline Excess	3,057,191
Total undiscounted reserves for loss and loss expenses, net of reinsurance		$	12,103,860

(In thousands)		December 31, 2020
Due from reinsurers on unpaid claims:
	Other liability	$	609,006
	Workers' compensation	267,707
	Professional liability	644,841
	Commercial automobile	32,140
	Short-tail lines	352,168
	Other	36,070
	Insurance	1,941,932
	Casualty	104,372
	Monoline excess	41,598
	Property	76,135
	Reinsurance & Monoline Excess	222,105
Total due from reinsurers on unpaid claims		$	2,164,037

(In thousands)		December 31, 2020
Loss reserve discount:
	Other liability	$	—
	Workers' compensation	(11,700)
	Professional liability	—
	Commercial automobile	—
	Short-tail lines	—
	Other	—
	Insurance	(11,700)
	Casualty	(100,536)
	Monoline excess	(371,231)
	Property	—
	Reinsurance & Monoline Excess	(471,767)
Total loss reserve discount		$	(483,467)
Total gross reserves for loss and loss expenses		$	13,784,430

Supplementary information regarding average historical claims duration

The following is supplementary information regarding average historical claims duration as of December 31, 2020:

Insurance
Average Annual Percentage Payout of Incurred Claims by Age, Net of Reinsurance
Years	1		2		3		4		5		6		7		8		9		10
Other liability	7.5	%	14.4	%	17.7	%	16.6	%	13.4	%	8.7	%	5.6	%	3.5	%	2.6	%	1.9	%
Workers' compensation	23.2	%	29.4	%	15.9	%	9.3	%	5.9	%	3.5	%	2.4	%	1.6	%	1.5	%	1.1	%
Professional liability	8.4	%	20.7	%	19.5	%	16.4	%	10.1	%	8.3	%	4.0	%	2.0	%	2.3	%	0.8	%
Commercial automobile	37.7	%	21.5	%	15.3	%	10.9	%	6.6	%	2.9	%	1.4	%	0.4	%	0.2	%	0.3	%
Short-tail lines	57.0	%	31.7	%	6.0	%	1.6	%	0.4	%	0.5	%	0.4	%	0.3	%	0.6	%	0.2	%
Reinsurance & Monoline Excess
Average Annual Percentage Payout of Incurred Claims by Age, Net of Reinsurance
Years	1		2		3		4		5		6		7		8		9		10
Casualty	6.5	%	11.7	%	14.1	%	14.0	%	11.5	%	8.9	%	6.5	%	4.7	%	4.9	%	3.9	%
Monoline excess	4.9	%	4.5	%	2.8	%	3.1	%	2.4	%	3.5	%	4.3	%	2.9	%	3.5	%	1.7	%
Property	33.3	%	33.2	%	15.4	%	6.0	%	3.9	%	2.2	%	1.6	%	1.2	%	0.8	%	0.6	%

Reconciliation of beginning and ending reserve balance

The table below provides a reconciliation of the beginning and ending reserve balances:

(In thousands)	2020		2019		2018
Net reserves at beginning of year	$	10,697,998	$	10,248,883	$	10,056,914
Cumulative effect adjustment resulting from changes in accounting principles (1)	5,927		—		—
Restated net reserves at beginning of period	10,703,925		10,248,883		10,056,914
Net provision for losses and loss expenses:
Claims occurring during the current year (2)	4,432,937		4,057,989		3,926,489
Increase in estimates for claims occurring in prior years (3)	627		34,079		6,831
Loss reserve discount accretion	35,142		39,048		41,382
Total	4,468,706		4,131,116		3,974,702
Net payments for claims:
Current year	921,054		985,599		964,808
Prior year	2,677,595		2,673,803		2,700,077
Total	3,598,649		3,659,402		3,664,885
Foreign currency translation	46,411		(22,599)		(117,848)
Net reserves at end of year	11,620,393		10,697,998		10,248,883
Ceded reserve at end of year	2,164,037		1,885,251		1,717,565
Gross reserves at end of year	$	13,784,430	$	12,583,249	$	11,966,448
Net change in premiums and losses occurring in prior years:
Increase in estimates for claims occurring in prior years (3)	$	(627)	$	(34,079)	$	(6,831)
Retrospective premium adjustments for claims occurring in prior years (4)	16,807		53,511		45,638
Net favorable premium and reserve development on prior years	$	16,180	$	19,432	$	38,807

_______________________________________

(1)The cumulative effect adjustment resulting from changes in accounting principals relates to the allowance for expected credit losses on reinsurance recoverables that commenced on January 1, 2020 due to the adoption of ASU 2016-13. See Note 1 for more details.

(2)Claims occurring during the current year are net of loss reserve discounts of $10 million, $20 million and $24 million in 2020, 2019, and 2018, respectively.

(3)The change in estimates for claims occurring in prior years is net of loss reserve discount. On an undiscounted basis, the estimates for claims occurring in prior years decreased by $21 million in 2020, increased by $19 million in 2019, and decreased by $4 million in 2018, respectively.

(4)For certain retrospectively rated insurance polices and reinsurance agreements, changes in loss and loss expenses for prior years are offset by additional or return premiums.