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Specific areas where actuarial judgment is required
- Determining optimal combinations of kinds of clms data to be used
- Assessing effect of chg in an insr operations on the claim data
- Adjusting clm data for influences of know and quantifiable events
- Evaluating the strenghts and weaknesses of various estimation techniques
- Making the final selection of the unpd clm estimate
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Chain Ladder / Dvpmt technique
- AssumptionsFuture clm dvpmt is similar to prior yrs dvpmt
- Clms observed for immature AY tell you something about clms yet to be observed
- Mechanics
- ObservationsDvpmt factors tend to increase as the retention increases
- When does it work+ large clm do not greatly distort data
- + high freq low sev
- - insufficient volume of credible data
- - leveraged effect of large clms
- Changing environment
- Responsive to inc CR, overstates when inc CO strenght
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Expected claims technique
- Assumptions
- Unpd clms can better be estimated based on a priori estimate than using experience observed to date
- Common uses
- Lines w. longer emergence and settlement patterns / New lob/terr / Operational or environemental chg / CL not appropriate / Data is unavailable
- MechanicsUlt clms = ECR * earned premium
- When does it work+ maitain stability over time
- - lack of responsiveness to recent experience
- Changing environmentUnderstate when inc CR, responsive to inc CO strength
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Bornhuetter-Ferguson Technique
- AssumptionsUnrpt clms will develop based on expected clms
- MechanicsUld clms = rpt + exp clms * (1 - 1 / CDF)
- When does it work+ rdm fluctuations at early maturities do not sign distort
- + used when data extremely thin or volatile or both
- - when CDF lt 1: have to limit to 1 or use other technique
- Changing environmentMust make delibarate chng in ECR to respond to inc CR
- Rpt BF will overstate when CO strenght inc, but less than CL
- Paid BF responsive to CO strenght chg
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Benktander Technique
- Credibility-weighted avg of BF and CL
- More responsive than BF and more stable than CL
- Uses BF estimate as initial expected losses to run BF again
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Cape Cod / Stanard-BuhlmannTechnique
- Reinsurers are most frequent users
- Assumptions
Urnpt clms will develop based on expected clms - MechanicsLike BF except for ECR (used-up premium)
- SB ECR = Σ(Rpt) / Σ(Adj EP * %Rpt)
- SB IBNR = ECR * Σ(Adj EP * (1 - %Rpt))
- When does it work+ rdm fluctuations at early maturities do not sign distort
- - not as appropriate as BF when data is thin
- - may be difficult to obtain adj prem
- Changing EnvironmentUnderstates when CR inc, but less than EC or BF
- Overstates by more than BF when chg in CO strength
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FS Techniques - Definition
- Proj ult clms by mult nbr clms * avg value
- Helps in understanding drivers in clm activity
- + examine trends and patterns
- + validate or reject findings
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FS Approach # 1 - Dvpmt
- AssumptionsConsistent def of clm cnt
- Clm cnt are reasonably homogeneous
- Clm cnt to date will continue to dvp in a similar manner
- MechanicsProject and select ult clm cnt and severity
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FS Approach # 2 - Incorporation of exposures and inflation
- AssumptionsTrend rates reflect economic and social inflation
- Trend rates vary by lob, geog, limits
- MechanicsCompare ult clm cnt to exposures and select freq
- Project severity
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FS Approach # 3 - Disposal Rate Technique
- AssumptionsDisposal rate = cum closed clm cnt / ult clm cnt
- Incr clm cnt = prev * (disp at y - disp at y-12) / (1 - disp at latest diag) * (ult clm cnt - closed to date)
- Multiply by incr severities
- When does it work
+ gain greater insight into clm process - + may be used w. paid clm data
- + ability to explicitely reflect inflation
- - highly sensitive to the inflation assumption
- - data needed may be unavailable
- - chgs in def of clm cnt
- - method relies on mix of clm to be relatively consistent
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CO Dvpmt Approach # 1 - Wiser
- AssumptionsClm activity related to IBNR is related consistently to clms already rpt
- Common usesWorks well w. clms-made coverage and RY analysis
- MechanicsUse ratio of incr pd to CO and ratio of CO to prev CO
- When does it work- future IBNR is not always related to clms already rpt
- - infrequent use and lack of benchmark
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CO Approach # 2
- AssumptionsOnly data available is CO
- Clms to date for self-insr will devp in a similar manner as industry benchmark
- MechanicsCO dev factor = (Rpt CDF - 1)(Paid CDF)/(Paid CDF - Rpt CDF) + 1
- LimitationsBenchmark may prove to be inaccurate
- Inappropriate for more recent yrs
- Individual large clms can distort
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Berquist-Sherman: Data selection
- Selection of substitute forms of data
- Use earned exposures instead of clm cnt
- Substitute PY for AY when limit or ded chg
- Substitute RY for AY when shift in social climate
- Substitute quarter for yr when growth shifts avg acc date
Subdivide loss exp into more homogeneous grps
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Berquist-Sherman - Data Adjustments
- Detect chg in case adequacy using
- Questions to clm dpmt mgmt
- Diagnostics (pd to rpt, avg CO, avg rpt, avg pd)
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Berquist-Sherman CO Adjustment
- Choose reference diagonal (last -> remain the same un/adj)
- Restate avg CO by trending back from latest diagonal
- Adj rpt = adj avg CO * open clm cnt + unadj paid
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Berquist-Sherman Pd clm dvpmt Adjustment
- Determine disposal rates
- Apply selected disposal rates to ult nb of clms to determine adj nb of closed clm cnt
- Derive paid clm corresponding to adj clm cnt (use regression analysis)
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Define salvage and subrogation
- Salvage: amt insr is able to collect from sale of damaged property acquired when paying insd for a total loss
- Subrogation: insr's right to recover the amt of clm pmt to a covered insd from a third party responsible for the injury or damage
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Evaluation of reserving techniques
- Should use more than 1 method (should incorporate credibility, regression analysis, data smoothing)
- Responsibility of the actuary to select most appropriate estimate from highly stable to highly responsive
- Actuary should explain significant differences between projections
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Formula for projected clms to emerge
Clms to emerge IBNR * (CDFx-y - 1) / (CDFx-ult - 1)
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Hugh White's question
- If rpt loss is higher than expected do you
- Reduce the bulk reserve by corresponding amt (EC)
- Leave the bulk reserve as same level (BF)
- Increase bulk reserve in proportion (CL)
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