Loss Adjustment Expense Reserving Adam D. Hartman, ACAS Casualty Loss Reserve Seminar September 14,...
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Transcript of Loss Adjustment Expense Reserving Adam D. Hartman, ACAS Casualty Loss Reserve Seminar September 14,...
Loss Adjustment Expense Reserving
Adam D. Hartman, ACAS
Casualty Loss Reserve Seminar
September 14, 1999
CLRS1999_ULAE.ppt
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Purpose To introduce basic reserving methodologies
for loss adjustment expenses that are not tracked on an accident year basis
To contrast different methodologies for allocating such reserves to accident year
CLRS1999_ULAE.ppt
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Discussion Topics Defining Terms (see Appendix) What’s Really Important Methodologies for Estimating Loss
Adjustment Expense Reserves Methodologies for Allocating LAE
Reserves to Accident Year Other Considerations
CLRS1999_ULAE.ppt
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What’s Really Important Identifying the components of LAE Understanding the way in which the
components are incurred Understanding the timing of the
corresponding expense payments
CLRS1999_ULAE.ppt
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LAE captured in accident year detail
Examples– External Legal Expenses– External Adjuster/Appraiser– Internal Legal Expenses (?)
Basic Methodologies– “chain-ladder” development– cumulative paid-to-paid– incremental paid-to-paid– generalized Cape Cod
CLRS1999_ULAE.ppt
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LAE captured at calendar year aggregate level Cannot be directly converted into accident
year triangles Basic Methodologies
– Transaction method (Brian)– “Classical” CY paid-to-paid– Kittel’s correction to “Classical”– Wendy Johnson method
CLRS1999_ULAE.ppt
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Transaction method
“ULAE” Reserve = Sum over t {X(t)*n(t)}
where– X(t) = Avg. cost of transaction t– n(t) = number of transaction type t required to close a
claim file (whether reported or not)– X(t) determined by time study– Var[X(t)] may be high– n(t) estimated using history
Very accurate, whole lotta work
CLRS1999_ULAE.ppt
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“Classical” Paid-to-Paid
Assumptions– 50% of ULAE paid at report – 50% of ULAE paid at close – ULAE outstanding is proportionate to losses
outstanding– Loss reserves are accurate– Age of claims does not affect p (see next slide)– ULAE, losses are paid at the same time and rate– Loss inflation% = ULAE inflation%
CLRS1999_ULAE.ppt
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“Classical” Paid-to-Paid
Paid-to-paid Ratio
PPR = Sum {CY Paid ULAE} Sum {CY Paid Losses}
(1-p) = % of “ULAE” unpaid on claims currently open.
50% paid at report,50% paid at close>>p=.5 Indicated “ULAE” Reserve
= PPR * [(1-p)*Case Reserve+ IBNR]
CLRS1999_ULAE.ppt
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“Classical” Paid-to-Paid
Appropriate only if…– line is short-tailed, stable– low/stable inflation– consistent claim reporting and closing patterns
For long-tail, rapidly-growing lines in high inflation– Historical (paid ULAE)/(paid loss) may be high– Classical Reserve > W Johnson Reserve
CLRS1999_ULAE.ppt
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Kittel’s Correction to “Classical” paid-to-paid Paid losses do not accurately represent work
done by Claims Dept.– do not account for opens during year still open at
December 31st
Replace [sum Paid ULAE/sum Paid losses] with
____Sum_Paid ULAE _
Sum[(1-p)*Paid Loss + p * Incd Loss]
CLRS1999_ULAE.ppt
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Kittel’s Assumptions
50% of ULAE incurred at report 50% of ULAE incurred at close ULAE is independent of age of claim ULAE and losses paid at same rate and time Loss reserves are accurate Same inflation% for losses & ULAE
CLRS1999_ULAE.ppt
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Richard Bill’s Revision to Kittel’s Conclusions
Inflation distorts the "Classical" 50/50 assumption regarding the payment of ULAE.
If high inflation, then % of ULAE paid at claim closure is significantly greater than % of ULAE paid at claim opening.
In a high inflation environment, the use of the 50/50 assumption tends to understate the ULAE reserve
This effect will be more pronounced the longer the payout pattern
CLRS1999_ULAE.ppt
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Factoring in Growth
If a company is growing rapidly in a low inflation environment, the use of the "Classical" paid-to-paid method will overstate the ULAE reserve
If longer payout pattern, then larger overstatement of reserves
Kittel's revised ratio produces a better ULAE reserve
CLRS1999_ULAE.ppt
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Factoring in Growth - continued
If a company is growing rapidly in a high inflation environment, the correct ratio is somewhere between the "Classical" ratio and Kittel's ratio depending upon the relative impact of exposure growth versus inflation.
CLRS1999_ULAE.ppt
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Wendy Johnson Method
General Concept– Forecast a workload measure (“weighted open
claims”) for settling current and prior accident years
– Forecast ULAE paid per unit of work– Do the math
CLRS1999_ULAE.ppt
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Wendy Johnson - Assumptions
ULAE incurred from time of reporting to time of closure
ULAE unrelated to nature of claim (it is a maintenance cost)
Effort associated with maintaining a claim file is twice as great during 1st year compared to subsequent years
CLRS1999_ULAE.ppt
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Wendy Johnson - Assumptions
No adjustment for claims closed during 1st year
Consistent claim reporting and disposal patterns
CLRS1999_ULAE.ppt
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Wendy Johnson - Step One
Calculate ULAE per “weighted open claim” during calendar year y
Ny= # pending claims at 12/31/y ny= # claims opened during calendar year y Weighted open claims = Ny + ny
ULAEy = calendar year y paid ULAE ULAE per weighted open claim for CY y =
ULAEy / (Ny + ny)
CLRS1999_ULAE.ppt
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Wendy Johnson - Modifications to Reflect Claims Closed Avg(#claims open @12/31/y,@12/31/y-1)
– or
assume all claims open @12/31/y will continue to be open throughout year y+1– or
assume that effort associated with maintaining a claim file is twice as great in both the year in which the claim is opened and the year it is closed.
CLRS1999_ULAE.ppt
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Modified W. Johnson - Example
Calendar Year Expense Per Weighted Claim
Calendar Year
Overhead Unallocated
LAE
Number of Outstanding
Claims
Number of Claims
ReportedNumber of
Claims ClosedWeighted
Claim Counts
Expense Per Weighted
Claim1990 124,300,000 78,700 1,294,000 1,280,000 1,692,700 73.431991 135,300,000 89,800 1,358,000 1,373,000 1,791,050 75.541992 146,800,000 99,100 1,397,000 1,400,000 1,846,100 79.521993 163,600,000 118,400 1,425,000 1,524,000 1,924,400 85.011994 166,600,000 142,300 1,513,000 1,610,000 2,057,800 80.961995 189,000,000 157,400 1,588,000 1,633,000 2,153,650 87.761996 210,700,000 172,400 1,657,000 1,695,000 2,253,150 93.511997 217,000,000 182,500 1,720,000 1,710,000 2,330,000 93.131998 242,700,000 226,000 1,860,000 1,820,000 2,541,000 95.51
Count WeightsReported 1.000
Outstanding 1.000Closes 0.250
CLRS1999_ULAE.ppt
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Wendy Johnson - Step 2a
UltClms(AYt ) = Ultimate Claims estimated for accident year t
%Rd=Cumulative % reported by dev. year d
%Cd=Cumulative % closed by dev. year d
Claims outstanding(AYt,@12/31/t+i)
= Nt,t+i = UltClms(AYt ) * (%Ri+1 - %Ri)
Claims opened(AYt,during CYt+i)
= nt,t+i = UltClms(AYt ) * (%Ri+1 - %Ci+1)
CLRS1999_ULAE.ppt
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Modified W. Johnson - Example
Selected Cumulative and Incremental Ratios12 24 36 48 60 72 84 96 108 120
Cum Reported 0.91420 0.98900 0.99550 0.99800 0.99920 0.99960 0.99990 1.00000 1.00000 1.00000Incr Reported 0.07480 0.00650 0.00250 0.00120 0.00040 0.00030 0.00010 0.00000 0.00000 0.00000Cum Closed 0.81350 0.98690 0.99400 0.99700 0.99840 0.99910 0.99950 0.99970 0.99990 1.00000Incr Closed 0.17340 0.00710 0.00300 0.00140 0.00070 0.00040 0.00020 0.00020 0.00010 0.00000
Ultimate CountsAccident Yr Ultimates
1984 228,7001985 263,2001986 296,8001987 321,3001988 332,3001989 339,1001990 334,2001991 331,6001992 337,4501993 355,3001994 362,7001995 347,6001996 357,2501997 349,1001998 355,300
CLRS1999_ULAE.ppt
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Modified W. Johnson - ExampleFuture Claims Reported
Accident Yr 12/1999 12/2000 12/2001 12/2002 12/2003 12/2004 12/2005 12/2006 12/20071990 0 0 0 0 0 0 01991 0 0 0 0 0 0 0 01992 50 0 0 0 0 0 0 0 01993 150 50 0 0 0 0 0 0 01994 250 187 62 0 0 0 0 0 01995 720 240 180 60 0 0 0 0 01996 1,139 547 182 137 46 0 0 0 01997 2,009 773 371 124 93 31 0 0 01998 27,549 2,394 921 442 147 110 37 0 0
Forecasted Claim counts adjusted for actuals, ergo, sum of forecasted + actuals to date = ultimate for each accident year
Future Claims ClosedAccident Yr 12/1999 12/2000 12/2001 12/2002 12/2003 12/2004 12/2005 12/2006 12/2007
1990 10 0 0 0 0 0 01991 20 10 0 0 0 0 0 01992 20 20 10 0 0 0 0 0 01993 133 67 67 33 0 0 0 0 01994 263 150 75 75 37 0 0 0 01995 607 303 173 87 87 43 0 0 01996 1,100 513 257 147 73 73 37 0 01997 2,222 939 438 219 125 63 63 31 01998 64,804 2,653 1,121 523 262 149 75 75 37
Forecasted Claim counts adjusted for actuals, ergo, sum of forecasted + actuals to date = ultimate for each accident year
Future Claims OutstandingAccident Yr 12/1999 12/2000 12/2001 12/2002 12/2003 12/2004 12/2005 12/2006 12/2007
1990 0 0 0 0 0 0 01991 10 0 0 0 0 0 0 01992 30 10 0 0 0 0 0 0 01993 117 100 33 0 0 0 0 0 01994 88 125 113 38 0 0 0 0 01995 213 150 157 130 43 0 0 0 01996 189 222 148 138 110 37 0 0 01997 487 321 253 158 126 94 31 0 01998 845 585 385 303 189 150 112 37 0
CLRS1999_ULAE.ppt
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Wendy Johnson - Step 2b
Projected Weighted Open Claims for CYy
WOCy= Sumt=all AY thru current{Nt,CYy + nt, CYy}
Fit historical ULAE per WOC through the current calendar year, x. a = annual trend
Project fitted values of ULAE per WOC for calendar year x+i
FVx+i = FVx * (1+a)i
CLRS1999_ULAE.ppt
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Modified W. Johnson - Example
Fitted Expense
Calendar Year
Adjusted Natural
LogarithmAdjusted Fitted
Expense Trend Factors1990 4.29637 73.85 Fitted 1.03451991 4.32469 76.40 Selected 1.0500
1992 4.37600 79.041993 4.44281 81.761994 4.39396 84.591995 4.47458 87.501996 4.53811 90.521997 4.53403 93.651998 4.55927 96.88
Trended ExpenseCalendar
YearTrended
Expenses12/1999 101.7212/2000 106.8112/2001 112.1512/2002 117.7612/2003 123.6412/2004 129.8312/2005 136.3212/2006 143.1312/2007 150.2912/2008 157.81
Future Weighted Claim CountsAccident Yr 12/1999 12/2000 12/2001 12/2002 12/2003 12/2004 12/2005 12/2006 12/2007
1990 2 0 0 0 0 0 01991 15 2 0 0 0 0 0 01992 85 15 2 0 0 0 0 0 01993 300 167 50 8 0 0 0 0 01994 403 350 194 56 9 0 0 0 01995 1,085 466 380 212 65 11 0 0 01996 1,603 897 394 311 174 55 9 0 01997 3,052 1,328 734 336 250 140 47 8 01998 44,594 3,642 1,586 876 402 298 168 56 9
CLRS1999_ULAE.ppt
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Wendy Johnson - Step 3
Projected ULAE paid in calendar year x+i on claims from accident years x and prior
UCYx+i,AY x&prior = WOCCYx+i,AY x&prior * FVx+i
Total ULAE reserve at 12/31/x
= Sumi=1 to end of tail{UCYx+i,AY x&prior }
CLRS1999_ULAE.ppt
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Modified W. Johnson - ExampleULAE Reserve
Accident Yr 12/1999 12/2000 12/2001 12/2002 12/2003 12/2004 12/2005 12/2006 12/20071990 254 0 0 0 0 0 01991 1,526 267 0 0 0 0 0 01992 8,646 1,602 280 0 0 0 0 0 01993 30,517 17,802 5,607 981 0 0 0 0 01994 41,007 37,383 21,729 6,624 1,159 0 0 0 01995 110,369 49,755 42,617 24,925 8,037 1,406 0 0 01996 163,039 95,832 44,206 36,636 21,500 7,140 1,250 0 01997 310,416 141,865 82,311 39,619 30,862 18,234 6,400 1,120 01998 4,536,265 389,033 177,827 103,165 49,675 38,675 22,852 8,024 1,404
Total 5,202,040 733,539 374,578 211,951 111,234 65,456 30,501 9,144 1,404
ULAE Totals
Accident YrAll Report
Years Total1984 01985 01986 01987 01988 01989 01990 2541991 1,7931992 10,5291993 54,9071994 107,9021995 237,1101996 369,6031997 630,8281998 5,326,920Total 6,739,846
CLRS1999_ULAE.ppt
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Estimating ULAE Reserve when Overhead Levels are Fixed Projected CYy paid ULAE for all AY
Uy,all AY=[CYx Paid ULAEall AY] * (1+alpha)y-x
where x = current CY, alpha = fixed growth%
CYx Paid ULAE may be fitted or actual
CLRS1999_ULAE.ppt
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Estimating ULAE Reserve when Overhead Levels are Fixed Projected CYy paid ULAE for AY x & prior
Uy,x&prior= Uy,all AY * WOCy,x&prior / WOCy,all AY
ULAE Reserve at 12/31/x
= Sumi=1 to end of tail{UCY x+i,AY x&prior}
CLRS1999_ULAE.ppt
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Advantages - W Johnson method
Flexibility: explicitly adjusts for change in– claims reporting and closure patterns– exposure growth– expense cost trends
Can be modified to assume ULAE payments in future years are fixed
Straightforward Uses relevant, readily available data
CLRS1999_ULAE.ppt
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Annual Statement Allocation of CY paid ULAE to AY
ULAE paid during the most recent calendar year are distributed to accident year as follows:
– (a) 45% to the most recent year
– (b) 5% to the next most recent year
– (c) the balance to all years, including the most recent, in proportion to the amount of loss payments (net of reinsurance) paid for each accident year during the most recent calendar year
– Exception: if the distribution in (a) or (b) produce an accumulated distribution to accident year > 10% of earned premium (net) for that year, excluding all distributions made under (c), such accumulated distribution should be limited to 10% of earned premiums and the balance distributed based on (c).
CLRS1999_ULAE.ppt
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Annual Statement Allocation of CY paid ULAE to AYAssumptions
50% of ULAE is paid when the claim is reported
50% of ULAE is paid when the claim is closed90% of claims are reported during the calendar
year when the accident occurred– 10% of claims are reported during the
following calendar year
CLRS1999_ULAE.ppt
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Annual Statement Allocation of CY paid ULAE to AYProblems with these Assumptions
Products Liability claims are often not reported until years after the accident date, and insurers spend significant time negotiating settlements and handling the claims. Statutory distribution assigns too much ULAE to
most recent years
CLRS1999_ULAE.ppt
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Annual Statement Allocation of CY paid ULAE to AYProblems with these Assumptions
Workers Comp permanent disability cases may have weekly indemnity payments extending over the disabled worker's lifetime.Statutory distribution assigns too little ULAE to
most recent years
CLRS1999_ULAE.ppt
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Distributing ULAE Reserves to Accident YearAnnual Statement contains no instructions
for distributing ULAE reserves to accident year.
If ULAE reserve can be distributed in same proportion as the quantity
Case Reserves + 2*IBNR Reserves
Then the reserves will have the advantage of anticipating future annual statement allocations of paid ULAE.
CLRS1999_ULAE.ppt
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Distributing ULAE Reserves to Accident YearAssumptions
IBNR claims are paid in the year they are reported"Bulk + IBNR" reserves consist of pure IBNR (no
provision for development on known claims is made in the IBNR reserves)
50% of ULAE is paid when the claim is reported50% of ULAE is paid when the claim is closed
These assumptions are generally not appropriate, but they are consistent with the Annual Statement allocation of paid ULAE
CLRS1999_ULAE.ppt
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Allocation of ULAE reserve to Accident Year - Wendy Johnson WOCx+i,t=Projected weighted open claims for
calendar year x+i, from accident year t
where x is current year and t < or = x
Indicated ULAE paid in CYx+i from AYt
UCY x+i,AY t=UCYx+i,AY x&prior * WOCCYx+i, AY t
WOCCYx+i,AY x&prior
ULAE Reserve at 12/31/x for AY t
= Sumi=1 to end of tail{UCY x+i,AY t}
CLRS1999_ULAE.ppt
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Distributing ULAE Reserves to Accident Year In a rapid growth / low inflation environment,
subsequent Annual Statement development will indicate that the ULAE reserve is...
Adequate, for the "Classical" paid-to-paid method (this is true regardless of environment)
Inadequate, for the Kittel adjustment methodInadequate, for the Wendy Johnson method
In reality, the Kittel and Wendy Johnson ULAE reserves will be more accurate.
CLRS1999_ULAE.ppt
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Other Considerations
Reinsurance Catastrophes Reserves for non-year-end financial
statements
CLRS1999_ULAE.ppt
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Conclusion: It bears repeating...
What’s Really Important– Identifying the components of LAE– Understanding the way in which the components are
incurred– Understanding the timing of the corresponding expense
payments
Additional reading– “Two Alternative Methods for Calculating the ULAE
Reserve”, Donald Mango & Craig Allen, CAS Forum, Fall 1999.
CLRS1999_ULAE.ppt
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Appendix
CLRS1999_ULAE.ppt
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Defining Terms An “LAE Reserve” should provide for the
ultimate expense required to settle outstanding claims as of the reserve date. (CAS Statement of Principles)
Loss Adjustment Expenses have been segregated into “Allocated” LAE and “Unallocated” LAE
CLRS1999_ULAE.ppt
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“Allocated” LAE For the 1996 Annual Statement and prior, NAIC
defined as all LAE that could be tied to a claim file.
External legal plus external adjuster and appraiser expenses
From the 1998 AS forward (‘97 optional), redefined: legal + medical cost containment
Renamed in 1999 AS, “Defense and Cost Containment”
CLRS1999_ULAE.ppt
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Defense & Cost Containment All litigation and medical cost containment
expenses, including…– surveillance expenses– fixed amounts for medical cost containment– litigation management expenses– LAE for participation in voluntary and
involuntary market pools if reported by accident year
CLRS1999_ULAE.ppt
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(more) Defense & Cost Containment Fees or salaries for appraisers, private
investigators, hearing representatives, reinspectors, & fraud investigators, if working in defense of a claim
Fees or salaries for rehab nurses, if not included in losses
Atty. Fees incurred owing to duty to defend Cost of engaging experts
CLRS1999_ULAE.ppt
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“Unallocated” LAE
For the 1996 AS and prior, NAIC defined as all LAE that could not be tied to a claim file.
Was company legal plus all other “non-allocated” LAE
From the 1998 AS forward (‘97 optional), ULAE excludes company legal expenses and includes external adj & appr
Renamed in 1999 AS, “Adjusting & Other”
CLRS1999_ULAE.ppt
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Adjusting & Other
LAE not within “Defense & Cost Containment”, including…– Fees of adjusters/settling agents– LAE for participation in voluntary and
involuntary market pools if reported by calendar year
– Atty. Fees incurred in determination of coverage, including litigation between insurer and policyholder
CLRS1999_ULAE.ppt
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(more) Adjusting & Other
– Fees/salaries of appraisers, private investigators, hearing representatives, reinspectors, and fraud investigators if working in the capacity of an adjuster
– “Standard unallocated” expenses such as salaries of Claims personnel and Loss Reserving staff, Claims’ share of rent and other overhead, etc.
CLRS1999_ULAE.ppt
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Reserve based upon Ultimate IncurredsTo reflect work on
Opening claims
Closing claims
Maintaining open claim files
Distribute CY(x) Paid ULAE to accident years in proportion to
Opening factor*[CY(x) Incd
Loss by AY]Closing factor*[CY(x) Paid
Loss by AY]
Open factor*[Average Loss Rsv by AY]
CLRS1999_ULAE.ppt
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Advantages of Reserve Based on Ultimate Incurred
Accounts for work on open files in a systematic manner
Self-adjusting (ultimate reflect changing factors, persistence)
Inflation-sensitive Reduces the effect of change in work
handled by independent and staff adj One method for ALAE and ULAE
CLRS1999_ULAE.ppt
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Disadvantages of Reserve Based on Ultimate Incurred
Requires some work to determine– percentage to assign each factor– percentage of LAE to distribute to Casualty
field adjusters and operations
CLRS1999_ULAE.ppt
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Annual Statement instructions unclear on distribution basisArgument in favor of using direct loss
payments to distribute paid ULAE to AYULAE are primarily related to direct loss paymentsAny reinsurance compensation for the ceding
insurer's ULAE is booked as offset to commissions, not to LAE
Argument in favor of using net loss payments to distribute paid ULAE to AY– It is common practice to use net loss payments