The Company's reserves for losses and loss expenses are comprised of case reserves and incurred but not reported liabilities (IBNR). When a claim is reported, a case reserve is established for the estimated ultimate payment based upon known information about the claim. As more information about the claim becomes available over time, case reserves are adjusted up or down as appropriate. Reserves are also established on an aggregate basis to provide for IBNR liabilities and expected loss reserve development on reported claims.

Loss reserves included in the Company’s financial statements represent management’s best estimates based upon an actuarially derived point estimate and other considerations. The Company uses a variety of actuarial techniques and methods to derive an actuarial point estimate for each operating unit. These methods may include paid loss development, incurred loss development, paid and incurred Bornhuetter-Ferguson methods and frequency and severity methods. In circumstances where one actuarial method is considered more credible than the others, that method is used to set the point estimate. The actuarial point estimate may also be based on a judgmental weighting of estimates produced from each of the methods considered. Industry loss experience is used to supplement the Company’s own data in selecting “tail factors” in areas where the Company’s own data is limited. The actuarial data is analyzed by line of business, coverage and accident or policy year, as appropriate, for each operating unit.

The establishment of the actuarially derived loss reserve point estimate also includes consideration of qualitative factors that may affect the ultimate losses. These qualitative considerations include, among others, the impact of re-underwriting initiatives, changes in claims handling procedures, changes in the mix of business, changes in distribution sources and changes in policy terms and conditions.

The key assumptions used to arrive at the best estimate of loss reserves are the expected loss ratios, rate of loss cost inflation, and reported and paid loss emergence patterns. Expected loss ratios represent management’s expectation of losses at the time the business is priced and written, before any actual claims experience has emerged. This expectation is a significant determinant of the estimate of loss reserves for recently written business where there is little paid or incurred loss data to consider. Expected loss ratios are generally derived from historical loss ratios adjusted for the impact of rate changes, loss cost trends and known changes in the type of risks underwritten. Expected loss ratios are estimated for each key line of business within each operating unit. Expected loss cost inflation is particularly important for the long-tail lines, such as excess casualty, and claims with a high medical component, such as workers’ compensation. Reported and paid loss emergence patterns are used to project current reported or paid loss amounts to their ultimate settlement value. Loss development factors are based on the historical emergence patterns of paid and incurred losses, and are derived from the Company’s own experience and industry data. The paid loss emergence pattern is also significant to excess and assumed workers’ compensation reserves because those reserves are discounted to their estimated present value based upon such estimated payout patterns.

Loss frequency and severity are measures of loss activity that are considered in determining the key assumptions described in our discussion of loss and loss expense reserves, including expected loss ratios, rate of loss cost inflation and reported and paid loss emergence patterns. Loss frequency is a measure of the number of claims per unit of insured exposure, and loss severity is a measure of the average size of claims. Factors affecting loss frequency include the effectiveness of loss controls and safety programs and changes in economic activity or weather patterns. Factors affecting loss severity include changes in policy limits, retentions, rate of inflation and judicial interpretations.

Another factor affecting estimates of loss frequency and severity is the loss reporting lag, which is the period of time between the occurrence of a loss and the date the loss is reported to the Company. The length of the loss reporting lag affects our ability to accurately predict loss frequency (loss frequencies are more predictable for lines with short reporting lags) as well as the amount of reserves needed for incurred but not reported losses (less IBNR is required for lines with short reporting lags). As a result, loss reserves for lines with short reporting lags are likely to have less variation from initial loss estimates. For lines with short reporting lags, which include commercial automobile, primary workers’ compensation, other liability (claims-made) and property business, the key assumption is the loss emergence pattern used to project ultimate loss estimates from known losses paid or reported to date. For lines of business with long reporting lags, which include other liability (occurrence), products liability, excess workers’ compensation and liability reinsurance, the key assumption is the expected loss ratio since there is often little paid or incurred loss data to consider. Historically, the Company has experienced less variation from its initial loss estimates for lines of businesses with short reporting lags than for lines of business with long reporting lags.

The most commonly used claim count method is by event. Most of the Company's operating units use the number of events to define and quantify the number of claims. However, in certain lines of business, where it is common for multiple parties to claim damages arising from a single event, an operating unit may quantify claims on the basis of the number of separate parties involved in an event. This may be the case with businesses writing substantial automobile or transportation exposure.

Claim counts for assumed reinsurance will vary based on whether the business is written on a facultative or treaty basis. Further variability as respects treaty claim counts may be reflective of the nature of the treaty, line of business coverage, and type of participation such as quota share or excess of loss contracts. Accordingly, the claim counts have been excluded from the below Reinsurance & Monoline Excess segment tables due to this variability.

The following tables present undiscounted incurred and paid claims development as of December 31, 2020, net of reinsurance, as well as cumulative claim frequency and the total of incurred but not reported liabilities (IBNR). The information about incurred and paid claims development for the years ended December 31, 2011 to 2019 is presented as supplementary information. To enhance the comparability of the loss development data, the Company has removed the impact of foreign exchange rate movements by using the December 31, 2020 exchange rate for all periods. Beginning with accident year 2012, the Company's U.K. and European insurance business is included in the Insurance segment's tables for Other Liability, Professional Liability, Commercial Automobile and Short-Tail Lines. Prior to 2012, the actuarial analysis for its U.K. and European insurance business was performed on an underwriting year basis and accident year data is not available for those years.


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


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


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


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


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


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


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


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


(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


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	%


(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

The ongoing COVID-19 global pandemic has impacted, and will likely continue to impact, the Company’s results through its effect on claim frequency and severity. Loss cost trends have been impacted and will likely be further impacted by COVID-19-related claims in certain lines of business, as well as by other effects of COVID-19 associated with economic conditions, inflation, and social distancing and work from home rules, for example. Although it is still too early to determine the net impact, it appears that the losses incurred due to COVID-19-related claims are being offset, to a certain extent, by lower claim frequency in certain lines of our businesses, including commercial auto, workers’ compensation, and other liability. However, given the continuing nature of the pandemic, the impact of COVID-19 could ultimately increase or decrease overall loss cost trends and is likely to have differing impacts on the Company's different lines of business.

Most of the COVID-19-related claims reported to the Company to date involve certain short-tailed lines of business, including contingency and event cancellation, business interruption, and film production delay. The Company expects additional claims to be reported for these lines of business. The Company has also received COVID-19-related claims for longer-tailed casualty lines of business such as workers’ compensation and other liability; however, the estimated incurred loss impact for these reported claims appears to be modest at this time. Given the continuing uncertainty regarding the pandemic's pervasiveness, the future impact that the pandemic may have on claim frequency and severity remains uncertain at this time. In workers’ compensation, for example, nearly two-thirds of the states have enacted rules, legislation or administrative orders creating a presumption that certain “essential”

workers who contract COVID-19 did so through the course of their employment. Several other states are considering similar actions, including varying the definition of “essential” workers. While the ultimate impact of these presumptions are unknown at this time, the Company believes that such state actions will likely increase workers’ compensation claims with respect to workers deemed “essential,” although this impact may be partially offset by lower workers’ compensation claim frequency with respect to non-essential workers.

The Company has estimated the potential COVID-19 impact to its contingency and event cancellation, workers’ compensation, and other lines of business under a number of possible scenarios; however, due to COVID-19’s evolving impact and the still limited amount of available data, there remains a high degree of uncertainty around the Company’s COVID-19 reserves. In addition, several states (and international jurisdictions), through regulation, legislation and/or judicial action, continue to seek to expand policy coverage terms beyond the policy’s intended coverage, including, for example, but not limited to, property coverages, where there are attempts to extend business interruption coverage where there is no physical damage or loss to property, and attempts to disregard policy exclusions for communicable disease. Accordingly, losses arising from these actions, and the other factors described above, could exceed the Company’s reserves established for those related policies.

For the year ended December 31, 2020, the Company recognized losses for COVID-19-related claims activity, net of reinsurance, of approximately $171 million, of which $161 million related to the Insurance segment and $10 million related to the Reinsurance & Monoline Excess segment. Such $171 million of COVID-19-related losses included $95 million of reported losses and $76 million of IBNR.

Insurance – Reserves for the Insurance segment developed favorably by $24 million in 2020 net of additional and return premiums). Continuing the pattern seen in recent years, the overall favorable development in 2020 resulted from more significant favorable development on workers’ compensation business, which was partially offset by unfavorable development on professional liability, including excess professional liability.

For workers’ compensation, the favorable development was spread across almost all prior accident years, including prior to 2011, but was most significant in accident years 2016 through 2019. The favorable workers’ compensation development reflects a continuation of the benign loss cost trends experienced during recent years, particularly the favorable claim frequency trends (i.e., number of reported claims per unit of exposure). The long term trend of declining workers’ compensation frequency can be attributable to improved workplace safety. Loss severity trends were also aided by our continued investment in claims handling initiatives such as medical case management services and vendor savings through usage of preferred provider networks and pharmacy benefit managers. Reported workers’ compensation losses in 2020 continued to be below our expectations at most of our operating units, and were below the assumptions underlying our initial loss ratio picks and our previous reserve estimates for most prior accident years.

For professional liability business, unfavorable development was driven mainly by large losses reported in the directors and officers (“D&O”), lawyers professional and excess hospital professional liability lines of business. For these lines of business, we continue to see an increase in the number of large losses reported and a lengthening of the reporting “tail” beyond historical levels. We believe a contributing cause is rising social inflation in the form of, for example, higher jury awards on cases that go to trial, and the corresponding higher demands from plaintiffs and higher values required to reach settlement on cases that do not go to trial. The unfavorable development for professional liability affected mainly accident years 2016 through 2018.

Reinsurance & Monoline Excess – Reserves for the Reinsurance & Monoline Excess segment developed unfavorably by $8 million in 2020. The unfavorable development in the segment was driven by non-proportional assumed liability business written in both the U.S. and U.K., and was partially offset by favorable development on excess workers’ compensation business. The unfavorable non-proportional assumed liability development was concentrated in accident years 2014 through 2018, and related primarily to accounts insuring construction projects and professional liability exposures.

Insurance - Reserves for the Insurance segment developed favorably by $21 million in 2019 (net of additional and return premiums). This overall favorable development resulted from more significant favorable development on workers’ compensation business, which was partially offset by unfavorable development on professional liability and general liability business.

For workers’ compensation, the favorable development was spread across many accident years, including prior to 2010, but was most significant in accident years 2014 through 2018, and particularly 2017 and 2018. The favorable workers’ compensation development reflects a continuation during 2019 of the benign loss cost trends experienced during recent years, particularly the favorable claim frequency trends (i.e., number of reported claims per unit of exposure). The long term trend of declining workers’ compensation frequency can be attributable to improved workplace safety. Loss severity trends were also aided by our continued

investment in claims handling initiatives such as medical case management services and vendor savings through usage of preferred provider networks and pharmacy benefit managers. Our initial loss ratio “picks” for this line of business over the past few accident years have contemplated an increase in loss cost trends and reflect decreasing premium rates in the marketplace; reported workers’ compensation losses in 2019 continued to be below our expectations at most of our operating units, and were below the assumptions underlying our initial loss ratio picks and our previous reserve estimates.

For professional liability business, the unfavorable development was driven mainly by an increase in the number of large losses reported in the lawyers professional liability and directors and officers (“D&O”) liability lines of business. Many of the lawyers large losses involved claims made against insured law firms relating to work performed on matters stemming from the 2008 financial crisis. These claims affected mainly accident years 2013 through 2016. In addition, for both of these lines of business, we have seen evidence of social inflation in the form of higher jury awards on cases that go to trial, and corresponding higher demands from plaintiffs and higher values required to reach settlement on cases that do not go to trial. The unfavorable development for D&O affected mainly accident years 2014 through 2017.

For general liability business, most of the unfavorable development emanated from our excess and surplus lines (E&S) businesses, and was driven by an increase in the number of large losses reported. Many of these large losses were from construction and contracting classes of business, which have also been impacted by social inflation. The general liability unfavorable development impacted mainly accident years 2015 through 2018.

Reinsurance & Monoline Excess - Reserves for the Reinsurance & Monoline Excess segment developed unfavorably by $2 million in 2019. The unfavorable development in the segment was driven by non-proportional assumed liability business in both the U.S. and U.K., and was largely offset by favorable development on excess workers’ compensation business. The unfavorable non-proportional assumed liability development was concentrated in accident years 2015 through 2018, and included an adjustment for the Ogden discount rate in the U.K.

For workers’ compensation, the favorable development was spread across many accident years, but was most significant in accident years 2015 through 2017. The favorable workers’ compensation development reflects a continuation during 2018 of the benign loss cost trends experienced during recent years, particularly the favorable claim frequency trends (i.e., number of reported claims per unit of exposure). The long term trend of declining workers' compensation frequency can be attributable to improved workplace safety. Loss severity trends were also aided by our continued investment in claims handling initiatives such as medical case management services and vendor savings through usage of preferred provider networks. Reported workers’ compensation losses in 2018 continued to be below our expectations at most of our operating units, and were below the assumptions underlying our previous reserve estimates.

For professional liability business, adverse development was primarily related to unexpected large directors and officers (“D&O”) liability losses at one of our U.S. operating units, as well as lawyers professional liability losses at another operating unit. The adverse development stemmed primarily from accident years 2015 and 2016, and was driven by a higher frequency of large losses than we had experienced in previous years.

Reinsurance & Monoline Excess - Reserves for the Reinsurance & Monoline Excess segment developed favorably by $20 million in 2018. The favorable development was primarily due to excess workers’ compensation business, and was spread across many accident years, including years prior to 2009. This favorable excess workers’ compensation development was partially offset by unfavorable development on U.S. casualty facultative assumed business from accident years 2009 and prior related to construction projects.

Environmental and Asbestos — To date, known environmental and asbestos claims have not had a material impact on the Company’s operations, because its subsidiaries generally did not insure large industrial companies that are subject to significant environmental or asbestos exposures prior to 1986 when an absolute exclusion was incorporated into standard policy language.

The Company’s net reserves for losses and loss expenses relating to asbestos and environmental claims on policies written before adoption of the absolute exclusion was $19 million at December 31, 2020 and $24 million at December 31, 2019. The estimation of these liabilities is subject to significantly greater than normal variation and uncertainty because it is difficult to make an actuarial estimate of these liabilities due to the absence of a generally accepted actuarial methodology for these exposures and the potential effect of significant unresolved legal matters, including coverage issues, as well as the cost of litigating the legal issues.

Discounting — The Company discounts its liabilities for certain workers’ compensation reserves. The amount of workers’ compensation reserves that were discounted was $1,655 million and $1,731 million at December 31, 2020 and 2019, respectively. The aggregate net discount for those reserves, after reflecting the effects of ceded reinsurance, was $483 million and $530 million at December 31, 2020 and 2019, respectively. At December 31, 2020, discount rates by year ranged from 0.7% to 6.5%, with a weighted average discount rate of 3.6%.

Substantially all discounted workers’ compensation reserves (97% of total discounted reserves at December 31, 2020) are excess workers’ compensation reserves. In order to properly match loss expenses with income earned on investment securities supporting the liabilities, reserves for excess workers’ compensation business are discounted using risk-free discount rates determined by reference to the U.S. Treasury yield curve. These rates are determined annually based on the weighted average rate for the period. Once established, no adjustments are made to the discount rate for that period, and any increases or decreases in loss reserves in subsequent years are discounted at the same rate, without regard to when any such adjustments are recognized. The expected loss and loss expense payout patterns subject to discounting are derived from the Company’s loss payout experience.

The Company also discounts reserves for certain other long-duration workers’ compensation reserves (representing approximately 3% of total discounted reserves at December 31, 2020), including reserves for quota share reinsurance and reserves related to losses regarding occupational lung disease. These reserves are discounted at statutory rates prescribed or permitted by the Department of Insurance of the State of Delaware.