

	Years Ended December 31,
(dollars in thousands)	2019			2018			2017
Net reserves for losses and loss adjustment expenses, beginning of year	$	9,214,443		$	8,964,945		$	8,108,717
Effect of foreign currency rate changes on beginning of year balance	18,857			(69,119		)	110,079
Adjusted net reserves for losses and loss adjustment expenses, beginning of year	9,233,300			8,895,826			8,218,796
Incurred losses and loss adjustment expenses:
Current accident year	3,426,441			3,371,699			3,367,223
Prior accident years	(535,307		)	(551,040		)	(497,627		)
Total incurred losses and loss adjustment expenses	2,891,134			2,820,659			2,869,596
Payments:
Current accident year	671,208			666,515			671,112
Prior accident years	1,979,032			1,835,027			1,513,580
Total payments	2,650,240			2,501,542			2,184,692
Effect of foreign currency rate changes on current year activity	1,067			(500		)	3,752
Net reserves for losses and loss adjustment expenses of acquired insurance companies	—			—			57,493
Net reserves for losses and loss adjustment expenses, end of year	9,475,261			9,214,443			8,964,945
Reinsurance recoverables on unpaid losses	5,253,415			5,062,036			4,619,336
Gross reserves for losses and loss adjustment expenses, end of year	$	14,728,676		$	14,276,479		$	13,584,281

In 2019, underwriting results included $100.4 million of underwriting loss from Hurricane Dorian and Typhoons Faxai and Hagibis (2019 Catastrophes). The underwriting loss on the 2019 Catastrophes was comprised of $114.0 million of net losses and loss adjustment expenses partially offset by $13.6 million of net assumed reinstatement premiums. The net losses and loss adjustment expenses on the 2019 Catastrophes were net of ceded losses of $62.5 million.

Incurred losses and loss adjustment expenses in 2019 included $535.3 million of favorable development on prior years' loss reserves, which included $431.0 million of favorable development on the Company's general liability, workers' compensation, professional liability and marine and energy product lines within the Insurance segment and property and whole account product lines within the Reinsurance segment. Favorable development within the Company's Insurance segment was primarily driven by lower loss severity than originally anticipated and a net decrease in open claims. Favorable development within the Company's Reinsurance segment was largely driven by lower than expected incurred and paid losses on reported claims.

In 2018, underwriting results included $287.3 million of underwriting loss from Hurricanes Florence and Michael, Typhoon Jebi and wildfires in California (2018 Catastrophes). The underwriting loss on the 2018 Catastrophes was comprised of $292.8 million of net losses and loss adjustment expenses partially offset by $5.4 million of net assumed reinstatement premiums. The net losses and loss adjustment expenses on the 2018 Catastrophe for the year ended December 31, 2018 were net of ceded losses of $244.1 million.

Incurred losses and loss adjustment expenses in 2018 included $551.0 million of favorable development on prior years' loss reserves, which included $424.1 million of favorable development on the Company's general liability, workers' compensation, professional liability and marine and energy product lines within the Insurance segment and credit and surety and marine and energy product lines within the Reinsurance segment. Favorable development within the Company's Insurance segment was primarily driven by lower claim frequency and lower loss severity than originally anticipated. Favorable development within the Company's Reinsurance segment was largely driven by lower than expected incurred and paid losses on reported claims.

In 2017, underwriting results included $565.3 million of underwriting loss from Hurricanes Harvey, Irma, Maria and Nate as well as the earthquakes in Mexico and wildfires in California (2017 Catastrophes). The underwriting loss on the 2017 Catastrophes was comprised of $585.4 million of net losses and loss adjustment expenses partially offset by $20.1 million of net assumed reinstatement premiums. The net losses and loss adjustment expenses on the 2017 Catastrophes for the year ended December 31, 2017 were net of ceded losses of $490.3 million.

Incurred losses and loss adjustment expenses in 2017 included $497.6 million of favorable development on prior years' loss reserves, which included $422.9 million of favorable development on the Company's general liability, marine and energy, professional liability, and workers' compensation product lines as well as personal lines business within the Insurance segment and property product lines within the Reinsurance segment. The favorable development within the Company's Insurance segment was primarily driven by favorable case incurred loss development and lower loss severity than originally anticipated. Favorable development within the Company's Reinsurance segment was due in part to lower than expected development on reported events, favorable claims settlements and lower than expected claims activity. The favorable development in 2017 was partially offset by $85.0 million of adverse development on the auto product line within the Reinsurance segment, resulting from a decrease in the discount rate, known as the Ogden Rate, used to calculate lump sum awards in United Kingdom (U.K.) bodily injury cases.

In 2017, the Company recognized a previously deferred gain of $3.9 million, which is included in losses and loss adjustment expenses in the consolidated statement of income and comprehensive income. This amount is excluded from the prior years' incurred losses and loss adjustment expenses for 2017 in the above table as the deferred gain was included in other liabilities on the consolidated balance sheet as of December 31, 2016, rather than unpaid losses and loss adjustment expenses.

The Company uses a variety of techniques to establish the liabilities for unpaid losses and loss adjustment expenses based upon estimates of the ultimate amounts payable. The Company maintains reserves for specific claims incurred and reported (case reserves) and reserves for claims incurred but not reported (IBNR reserves), which include expected development on reported claims. The Company does not discount its reserves for losses and loss adjustment expenses to reflect estimated present value, except for reserves held for a runoff book of U.K. motor business. Additionally, reserves assumed in connection with an acquisition are recorded at fair value at the acquisition date. The fair value adjustment includes an adjustment to reflect the acquired reserves for losses and loss adjustment expenses at present value plus a risk premium, the net of which is amortized to losses and loss adjustment expenses within the consolidated statements of income.

There is normally a time lag between when a loss event occurs and when it is actually reported to the Company. The actuarial methods that the Company uses to estimate losses have been designed to address the lag in loss reporting as well as the delay in obtaining information that would allow the Company to more accurately estimate future payments. There is also a time lag between cedents establishing case reserves and re-estimating their reserves, and notifying the Company of the new or revised case reserves. As a result, the reporting lag is more pronounced in reinsurance contracts than in the insurance contracts due to the reliance on ceding companies to report their claims. On reinsurance transactions, the reporting lag will generally be 60 to 90 days after the end of a reporting period, but can be longer in some cases. Based on the experience of the Company's actuaries and management, loss development factors and trending techniques are selected to mitigate the difficulties caused by reporting lags. The loss development and trending factor selections are evaluated at least annually and updated using cedent specific and industry data.

IBNR reserves are based on the estimated ultimate cost of settling claims, including the effects of inflation and other social and economic factors, using past experience adjusted for current trends and any other factors that would modify past experience. IBNR reserves are generally calculated by subtracting paid losses and loss adjustment expenses and case reserves from estimated ultimate losses and loss adjustment expenses. IBNR reserves were 65% of total unpaid losses and loss adjustment expenses at December 31, 2019 compared to 64% at December 31, 2018.

In establishing liabilities for unpaid losses and loss adjustment expenses, the Company's actuaries estimate an ultimate loss ratio, by accident year or policy year, for each product line with input from underwriting and claims personnel. For product lines in which loss reserves are established on a policy year basis, the Company has developed a methodology to convert from policy year to accident year for financial reporting purposes. In estimating an ultimate loss ratio for a particular line of business, the actuaries may use one or more actuarial reserving methods and select from these a single point estimate. To varying degrees, these methods include detailed statistical analysis of past claim reporting, settlement activity, claim frequency and severity, policyholder loss experience, industry loss experience and changes in market conditions, policy forms and exposures. Greater judgment may be required when new product lines are introduced or when there have been changes in claims handling practices, as the statistical data available may be insufficient. These estimates also reflect implicit and explicit assumptions regarding the potential effects of external factors, including economic and social inflation, judicial decisions, changes in law, general economic conditions and recent trends in these factors. Management believes the process of evaluating past experience, adjusted for the effects of current developments and anticipated trends, is an appropriate basis for predicting future events.

Estimates for losses from widespread catastrophic events are based on claims received to date, detailed policy and reinsurance contract level reviews, industry loss estimates and output from both industry and proprietary models. Due to the inherent uncertainty in estimating such losses, these estimates are subject to variability, which increases with the severity and complexity of the underlying event. As additional claims are reported and paid, and industry loss estimates are revised, the Company incorporates this new information into its analysis and adjusts its estimate of ultimate losses and loss adjustment expenses. For example, both the gross and net losses on the 2019, 2018 and 2017 Catastrophes as of December 31, 2019 represent the Company's best estimates based upon information currently available. For the 2019 Catastrophes, these estimates are still dependent on broad assumptions about coverage, liability and reinsurance. While the Company believes the reserves for the 2019, 2018 and 2017 Catastrophes as of December 31, 2019 are adequate, it continues to closely monitor reported claims and will adjust estimates of gross and net losses as new information becomes available.

Loss reserves are established at management's best estimate, which is generally higher than the corresponding actuarially calculated point estimate. The actuarial point estimate represents the actuaries' estimate of the most likely amount that will ultimately be paid to settle the losses that have occurred at a particular point in time; however, there is inherent uncertainty in the point estimate as it is the expected value in a range of possible reserve estimates. In some cases, actuarial analyses, which are based on statistical analysis, cannot fully incorporate all of the subjective factors that affect development of losses. In other cases, management's perspective of these more subjective factors may differ from the actuarial perspective. Subjective factors where management's perspective may differ from that of the actuaries include: the credibility and timeliness of claims information received from third parties, economic and social inflation, judicial decisions, changes in law, changes in underwriting or claims handling practices, general economic conditions, the risk of moral hazard and other current and developing trends within the insurance and reinsurance markets, including the effects of competition. As a result, the actuarially calculated point estimates for each of line of business represents starting points for management's quarterly review of loss reserves.

Inherent in the Company's reserving practices is the desire to establish loss reserves that are more likely redundant than deficient. As such, the Company seeks to establish loss reserves that will ultimately prove to be adequate. As part of the Company's acquisition of insurance operations, to the extent the reserving philosophy of the acquired business differs from the Company's reserving philosophy, the post-acquisition loss reserves will be strengthened until total loss reserves are consistent with the Company's target level of confidence. Furthermore, the Company's philosophy is to price its insurance products to make an underwriting profit. Management continually attempts to improve its loss estimation process by refining its ability to analyze loss development patterns, claim payments and other information, but uncertainty remains regarding the potential for adverse development of estimated ultimate liabilities.

b)The following tables present undiscounted loss development information, by accident year, for the Company's Insurance and Reinsurance segments, including cumulative incurred and paid losses and allocated loss adjustment expenses, net of reinsurance, as well as the corresponding amount of IBNR reserves as of December 31, 2019. This level of disaggregation is consistent with how the Company analyzes loss reserves for both internal and external reporting purposes. The loss development information for the years ended December 31, 2012 through 2018 is presented as supplementary information. Incurred losses in both our Insurance and Reinsurance segments generally remain outstanding more than eight years; however, data prior to 2012 is not practically available by segment as a result of a change in the Company's reportable segments in 2014. Additionally, reserves for the Company's international operations are determined on a policy year basis and historical data prior to 2012 does not exist by accident year. All amounts included in the tables below related to transactions denominated in a foreign currency have been translated into U.S. Dollars using the exchange rates in effect at December 31, 2019.

The difference between the segment loss development implied by the tables for the year ended December 31, 2019 and actual losses and loss adjustment expenses on prior accident years for the Insurance and Reinsurance segments for the year ended December 31, 2019 is primarily attributed to the fact that amounts presented in these tables exclude amounts attributed to the 2011 and prior accident years. Favorable development on 2011 and prior accident years for the year ended December 31, 2019 totaled $46.9 million, or 10% of total incurred losses and loss adjustment expenses on prior accident years, for the Insurance segment. Favorable development on 2011 and prior accident years for the year ended December 31, 2019 totaled $43.0 million for the Reinsurance segment. For the Reinsurance segment, this favorable development was primarily due lower than expected paid and incurred losses on reported claims within the segment's whole account product line, on the 2006 to 2008 accident years, and on its professional liability product lines across multiple accident years. Within the Company's professional liability product lines, the favorable development on 2011 and prior accident years was largely offset by an increase in losses and loss adjustment expenses on the 2017 and 2018 accident years as a result of net favorable premium adjustments in 2019, for which the related incurred losses were attributed to the 2017 and 2018 accident years.

The remaining difference between the segment loss development implied by the tables for the year ended December 31, 2019 and actual losses and loss adjustment expenses on prior accident years is attributed to the fact that amounts presented in these tables exclude unallocated loss adjustment expenses and exclude amounts attributable to reserve discounting and fair value adjustments recorded in conjunction with acquisitions, as well as differences in the presentation of foreign currency movements, as described above, none of which are material to the Insurance or Reinsurance segments.

The Insurance segment table below also includes claim frequency information, by accident year. The Company defines a claim as a single claim incident, per policy, which may include multiple claimants and multiple coverages on a single policy. Claim counts include claims closed without a payment as well as claims where the Company is monitoring to determine if an exposure exists, even if a reserve has not been established.

All of the business contained within the Company's Reinsurance segment represents treaty business that is assumed from other insurance or reinsurance companies, for which the Company does not have access to the underlying claim counts. Further, this business includes both quota share and excess of loss treaty reinsurance, through which only a portion of each reported claim results in losses to the Company. As such, the Company has excluded claim count information from the Reinsurance segment disclosures.

In 2013, the Company completed the acquisition of Alterra Capital Holdings Limited (Alterra), the results of which are included in both of the Company's reportable segments. Ultimate incurred losses and loss adjustment expenses, net of reinsurance as of December 31, 2013 include outstanding liabilities for losses and loss adjustment expenses of Alterra as of the acquisition date, by accident year, and not in any prior periods. Pre-acquisition data is not available by segment and accident year due in part to the impact of significant intercompany reinsurance contracts. Additionally, Alterra reserves were historically determined on a policy year basis and pre-acquisition data does not exist in a format that can be used to determine accident year. Following the acquisition, ongoing business attributable to Alterra was integrated with the Company's other insurance operations and is not separately tracked.



(dollars in millions)	Ultimate Incurred Losses and Allocated Loss Adjustment Expenses, Net of Reinsurance																Total of Incurred-but-Not-Reported Liabilities, Net of Reinsurance		Cumulative Number of Reported Claims
	Unaudited														As of December 31,
	As of December 31,																		(in thousands)
Accident Year	2012		2013		2014		2015		2016		2017		2018		2019		December 31, 2019
2012	$	1,370.8	$	1,613.2	$	1,491.6	$	1,430.2	$	1,397.8	$	1,364.1	$	1,350.7	$	1,330.5	$	101.3	128
2013			1,738.0		1,698.2		1,528.4		1,464.9		1,418.1		1,372.0		1,329.3		126.7		88
2014					1,866.0		1,700.1		1,632.2		1,574.2		1,525.7		1,505.3		138.6		80
2015							1,786.6		1,714.2		1,591.7		1,537.3		1,505.4		197.1		85
2016									1,875.3		1,872.1		1,770.8		1,716.5		297.3		90
2017											2,330.8		2,198.9		2,076.2		422.4		124
2018													2,457.3		2,354.8		904.0		173
2019															2,582.3		1,639.8		181
Total															$	14,400.3

	Cumulative Paid Losses and Allocated Loss Adjustment Expenses, Net of Reinsurance
	Unaudited														As of December 31,
	As of December 31,
Accident Year	2012		2013		2014		2015		2016		2017		2018		2019
2012	$	233.8	$	568.6	$	781.5	$	939.5	$	1,055.0	$	1,119.8	$	1,153.2	$	1,180.1
2013			271.8		572.1		780.0		950.5		1,038.9		1,101.3		1,125.1
2014					332.3		659.2		896.5		1,064.7		1,170.5		1,255.3
2015							322.8		666.0		877.7		1,041.9		1,151.9
2016									372.5		753.7		983.7		1,169.8
2017											438.8		992.8		1,286.7
2018													496.7		1,027.8
2019															527.9
Total															$	8,724.6
All outstanding liabilities for unpaid losses and loss adjustment expenses before 2012, net of reinsurance															365.7
Total liabilities for unpaid losses and loss adjustment expenses, net of reinsurance															$	6,041.4

Ultimate incurred losses and allocated loss adjustment expenses as of December 31, 2013 for the Insurance segment include $256.5 million and $313.4 million of losses and loss adjustment expenses on the 2012 and 2013 accident years, respectively, attributable to Alterra. Cumulative paid losses and allocated loss adjustment expenses as of December 31, 2013 include $36.8 million and $29.5 million of paid losses and allocated loss adjustment expenses on the 2012 and 2013 accident years, respectively, attributable to the acquired Alterra reserves and post-acquisition Alterra business. Cumulative paid losses and allocated loss adjustment expenses and cumulative reported claims for the 2012 and 2013 accident years exclude any claims paid or closed prior to the acquisition.

Variability in claim counts is primarily attributable to claim counts associated with a personal lines product with high claim frequency and low claim severity. Cumulative reported claims for the 2012, 2013, 2017, 2018 and 2019 accident years include 66 thousand, 17 thousand, 24 thousand, 54 thousand and 78 thousand, respectively, of claim counts associated with this product. The Company did not write this business from 2014 to 2016. The related net incurred losses and allocated loss adjustment expenses are not material to the Insurance segment.



	Ultimate Incurred Losses and Allocated Loss Adjustment Expenses, Net of Reinsurance																Total of Incurred-but-Not-Reported Liabilities, Net of Reinsurance
	Unaudited														As of December 31,
(dollars in millions)	As of December 31,
Accident Year	2012		2013		2014		2015		2016		2017		2018		2019		December 31, 2019
2012	$	73.0	$	551.7	$	508.7	$	486.6	$	457.8	$	456.2	$	448.0	$	445.1	$	42.4
2013			588.0		580.3		548.3		534.7		544.8		507.5		489.4		42.7
2014					577.4		564.5		536.4		581.2		559.1		535.4		87.7
2015							527.9		514.0		532.4		523.5		511.9		143.4
2016									522.1		532.1		530.6		529.3		126.6
2017											905.3		938.1		943.1		276.1
2018													759.2		792.5		373.4
2019															678.2		483.1
Total															$	4,924.9

	Cumulative Paid Losses and Allocated Loss Adjustment Expenses, Net of Reinsurance
	Unaudited														As of December 31,
	As of December 31,
Accident Year	2012		2013		2014		2015		2016		2017		2018		2019
2012	$	4.1	$	64.7	$	129.1	$	184.3	$	232.0	$	264.4	$	289.5	$	309.5
2013			71.3		155.7		209.9		268.9		301.9		331.9		351.0
2014					98.0		158.1		226.4		274.5		311.8		346.0
2015							63.8		133.4		207.2		258.5		306.2
2016									79.7		170.4		241.5		298.3
2017											158.0		359.5		481.5
2018													87.5		256.7
2019															54.1
Total															$	2,403.3
All outstanding liabilities for unpaid losses and loss adjustment expenses before 2012, net of reinsurance															553.5
Total liabilities for unpaid losses and loss adjustment expenses, net of reinsurance															$	3,075.1

Ultimate incurred losses and allocated loss adjustment expenses as of December 31, 2013 for the Reinsurance segment include $476.2 million and $537.5 million of losses and loss adjustment expenses on the 2012 and 2013 accident years, respectively, attributable to Alterra. Cumulative paid losses and allocated loss adjustment expenses as of December 31, 2013 include $52.7 million and $68.7 million of paid losses and allocated loss adjustment expenses on the 2012 and 2013 accident years, respectively, attributable to the acquired Alterra reserves and post-acquisition Alterra business. Cumulative paid losses and allocated loss adjustment expenses for the 2012 and 2013 accident years exclude any claims paid prior to the acquisition.



(dollars in thousands)	December 31, 2019
Net outstanding liabilities
Insurance segment	$	6,041,424
Reinsurance segment	3,075,109
Other underwriting	134,299
Program services and other	2,224
Liabilities for unpaid losses and loss adjustment expenses, net of reinsurance	9,253,056

Reinsurance recoverable on unpaid losses
Insurance segment	1,838,552
Reinsurance segment	349,124
Other underwriting	155,714
Program services and other	2,910,025
Total reinsurance recoverable on unpaid losses	5,253,415

Unallocated loss adjustment expenses	264,029
Unamortized discount, net of acquisition fair value adjustments, included in unpaid losses and loss adjustment expenses	(41,824		)
	222,205
Total gross liability for unpaid losses and loss adjustment expenses	$	14,728,676

c)The Company has exposure to asbestos and environmental (A&E) claims primarily resulting from policies written by acquired insurance operations before their acquisition by the Company. The Company's exposure to A&E claims originated from umbrella, excess and commercial general liability insurance policies and assumed reinsurance contracts that were written on an occurrence basis from the 1970s to mid-1980s. Exposure also originated from claims-made policies that were designed to cover environmental risks provided that all other terms and conditions of the policy were met. A&E claims include property damage and clean-up costs related to pollution, as well as personal injury allegedly arising from exposure to hazardous materials. Development on A&E loss reserves is monitored separately from the Company's ongoing underwriting operations and is not included in a reportable segment.

The Company's reserves for losses and loss adjustment expenses related to A&E exposures represent management's best estimate of ultimate settlement values based on statistical analysis of these reserves by the Company's actuaries. A&E exposures are subject to significant uncertainty due to potential loss severity and frequency resulting from the uncertain and unfavorable legal climate. A&E reserves could be subject to increases in the future, however, management believes the Company's gross and net A&E reserves at December 31, 2019 are adequate.