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Development: What, why, how?

Three causes of development

  • Development of known claims: e.g. case reserves are too low or too high on existing claims
  • New claims being reported: e.g. late reported claims
  • Closed claims being re-opened: e.g. additional payments on existing claims

Age-to-age Factor Selection

\(\to\) \(\downarrow\) data \(\Delta\) Future?

  1. Smooth progression (down) across columns: \(\to\)
  2. Stability (=) of factors in the same column: \(\downarrow\)
  3. Credibility of experience: limited data? Use industry benchmark
  4. Change in patterns: systematic patterns \(\Delta\) operations/environment
  5. Is it applicable to future development?

Misc.

  • CY Paid losses from AY \(\Delta\) \(\to\) Diagonal of Incremental Paid losses.
  • Settlement rate = \(\dfrac{\text{Closed claim \# a/o given maturity of AY}}{\text{Ultimate claim counts of AY}}\)a
    • Speedup means: claims will move from case reserves to paid claims 1:1… so net effect on reported losses = 0
    • If reported losses also changed \(\implies\) Case Reserve Adequacy has changed
  • Case Reserve Adequacy = \(\dfrac{\text{Total case reserves on all claims}}{\text{Ultimate claims estimate}}\)
    • Strengthening means the insurer has higher case reserves than in the past. He is recognizing the IBNR component, and is setting more reserves.
    • Since the movement is from IBNR reserves (which isn't part of reported claims) \(\to\) case reserves, the value reported losses have changed.
  • Tail factor
    • When? When we observe an age-to-age factor greater than 1 in the last development period
    • How?
      • Use industry tail factors
      • Fit a curve to the development factors and extrapolate the tail factor

Overlap fallacy

  • There is no overlap between loss development and loss trend
  • Loss development
    • makes sure that the future policy is priced to cover ultimate losses. Pricing is the point
    • takes losses from the average accident date at the future period to their ultimate levels.
  • Trending
    • makes sure that the ultimate losses are at the cost levels corresponding to the future policy period.
    • Hist. losses are trended from the average accident date of the historical period to the average accident date of the future period.

Chain Ladder

  • (Theory)
    • Tail factors beyond last month?
      Fit a curve to the development factors and extrapolate a tail factor

  • Will CL work?

    • Increasing trends in the Claim ratios. ✅
    • If average paid claims are increasing YoY at a stable rate ✅

  • Reserve Valuation 4-phase approach

    1. Exploratory analysis: find anomalies, balancing data to other verified sources
    2. Applying appropriate techniques for estimating unpaid claims
    3. Evaluating the conflicting results of the various methods:
      • Reconcile or explain different outcomes.
      • Evaluate ultimate estimates outside their original frame of analysis
    4. Monitoring projections of claim development over subsequent calendar periods
      • Looking at deviations between the actual vs the expected as a diagnostic tool.

Wording

  • Changing LR #doubt (what is it exactly?)
  • Incurred claims = Reported losses2
  • When found a change… like CSR, CRA
    • If you noticed that there is a increase in the YoY paid claims %
      • Say Since the paid loss growth in AY XX is substantially more than the growth in premiums, this could be indicative of increase in claim settlement rates or a deterioration of results.
      • Then assume that it is the first… and say If it is caused by a speedup in claims handling, then using Paid LDFs from past years will overstate the ultimate losses of AY XX8
    • If you noticed that the YoY \(\dfrac{\text{Paid Claims}}{\text{Reported Claims}}\) is decreasing down the first column. (2010 (E6) - 15)
      • Say Since the ratio of cum paid claims to cum reported claims is decreasing down the columns, this could be indicative of decrease in claim settlement rates. Alternatively, it could be due to increase in case reserve adequacy.
      • Or if really so, then say… since the data is very small, there is little credibility to draw conclusions from9
  • How to write impact of distortions. Samples:
    • All the existing open claims of AY 2006 will be less than 18 months old as of the valuation date 12/31/2016, they will have a case reserve of 5000 each. The historical development patterns assumed that the case reserves would have been 10,000 and as such those development **patterns would project developments based on those higher prior case reserves. (Personify the "patterns")
    • Est Ultimate losses would be overstated since the reported loss development would have assumed the same lower case reserve adequacy that appeared in the past years.

Development technique (general assumptions)

  1. Development of future claims will be similar to development in prior periods
    • Think of \(\to\) \(\to\) \(\to\) going \(\uparrow\) \(\uparrow\)
    • Other assumptions (implicit)12
      • Consistent claims processing (over time)
        • Claims handling, setting reserves (CRA) \(\impliedby\) Rept Dev
        • Claims handling, settlement rates (CRS) \(\impliedby\) Paid Dev
      • Stable mix of types of claims
      • Stable policy limits and deductibles
      • Stable reinsurance limits (if looking at net)
  2. Claims observed for an immature period tell you something about claims yet to be observed
    • Latest rept tells you about IBNR

Diagnostics

Triangles

Observe Deduce Remarks
\(\dfrac{\text{Closed \#}}{\text{Rept}\#}\) CSR Use this first, its sure-shot way to tell if CSR increased or decreased. DON'T MISTAKE using using the paid/rept amounts ratio.
\(\dfrac{\text{Closed w/o Pay \#}}{\text{Closed \#}}\) % of claims being closed w/o pay
\(\text{Avg Paid}\) 1. Severity trends
2. CSR (small vs large)
\(\text{Avg Case Reserves}\) 1. CRA
2. CSR (small vs large)
\(\dfrac{\text{Paid Loss}}{\text{Rept Loss}}\) 1. CSR
2. CRA		 Decreasing down YoY \(\implies\)
- Slowdown in claims
- increase in CRA
YoY Paid Claims % 1. CSR
2. Growth rate / Trend
### Changes and Diagnostic triangles

Problems

  • 1998 Exam 6 - Q58
  • 2011 Exam 5 - Q36

Situations

  • A new court gets added: Claims will settle faster \(\to\) The initial paid and reported claims for new years will be higher \(\to\) Paid and Rept development will overestimate
  • "Caps on […] liability lawsuits" \(\to\) Lawsuits tend to get resolved in later maturities. The paid and probably13 reported claims will likely be similar to historical values in the earlier maturities, but reduced in the later maturities \(\to\) Unadjusted paid and reported dev will overestimate
  • Increase in limits (say from $500K to $1M) will lead to higher paid and reported amounts at later maturities as the largest claims are settled \(\to\) Unadjusted paid and rept dev will understate
  • Strategy

  • Josh says
    > “My personal preference to understand loss data changes is to first look at triangles that have the least reasons to show changes and then look at triangles that have the most reasons to show changes. As such, I like to start looking at reported claim counts, since they would usually only be impacted by changes in claim frequency or claim reporting patterns.
    > Next, I would move on to looking at \(\dfrac{\text{Closed Claim \#}}{\text{Rept Claim \#}}\) to see if there have been any changes in the settlement rate of claims. Then I would look at paid losses and/or average paid amounts, and finally I’d look at reported losses and/or average reported amounts.” (pdf) - Josh

    1. First check which triangle columns are "stable" and state them.
      • e.g. Reported # triangle is stable \(\implies\) no significant change in claim reporting pattern
    2. Try to state the most obvious patterns from
    3. You might want to combine the observations of two and see what it entails.

Deductions

  • Observations
    1. \(\dfrac{\text{Closed \#}}{\text{Rept \#}}\) % \(\uparrow\) \(\implies\) CSR \(\uparrow\)15
    2. \(\text{Avg Paid}\) \(\downarrow\) \(\implies\) The claims that are being closed are smaller, and thus \(\dfrac{\text{Paid (made of small claims)}}{\text{Paid \#}}\) is small.
    3. \(\text{Avg Case O/S}\) \(\uparrow\) \(\implies\) Smaller claims are closed and we are left with the larger claims, thus \(\dfrac{\text{Case O/S (remaining large claims)}}{\text{Open \#}}\) is large.
  • Observation: \(\dfrac{\text{Closed \#}}{\text{Rept \#}}\) % \(\uparrow\) \(\implies\) CSR \(\uparrow\)
    • More info: Paid claims didn't increase as much (commensurately) \(\implies\) smaller claims are being closed faster OR avg paid claims \(\downarrow\)
    • \(\implies\) SR \(\uparrow\) for smaller claims4
  • Observation: Increase in incremental incurred losses (= paid + case reserves)
    1. This increase \(\gt\) increase in paid claims \(\implies\) increase is due to increase in case reserves
    2. Stable reported claim counts \(\implies\) increase in CR not due to more claim counts \(\implies\) increase in CRA
    3. \(\implies\) Increase in CRA

Mechanisms

  • Situation: For property claims, a new claims processing system is implemented that will result in claims closing faster.
    • Faster claims processing \(\implies\) open claim counts will increase. But note that this doesn't reduce the average case outstanding
    • Avg case outstanding changes only if the priority of small vs large claims settlement changes.
    • GENERALLY, the scenario is that small claims will close faster: if so the remaining open claims will be larger on average \(\implies\) Larger case outstanding values
  • Situation: For liability claims, a tort reform change is passed that will reduce the statute of limitations on reporting a claim
  • Situation: Claims department staffing has reduced
  • Situation: Insurer decides to litigate14
  • Situation: Increase in SR for smaller claims
    • Side effects: remaining open claims will be the larger claims \(\implies\) avg case reserve should increase.
    • But total case reserves will not increase.
    • e.g. (CRA and SR work in opposite directions for total case reserves)
      • Init:
        • paid = 3 x 2000 = 6000
        • avg paid = 2000
        • total case reserves 2 x 1000 + 5 x 5000 = 27000
        • avg case reserves = 27000/7 =3875
      • After speedup of smaller claim settlement rates
        • paid = 3 x 2000 + 2 x 1000 = 8000
        • avg paid = 8000/5 = 1600 (\(\downarrow\) )
        • total case reserves = 5 x 5000 = 25000 (\(\downarrow\) )
        • avg case reserves = 25000/5 = 5000 (\(\uparrow\))
      • Total case reserves reduced3
      • But had it increased, we could suspect that there has been an increase in the case reserve adequacy.

Questions to management

  • Takes more time to settle a claim after reporting (Increased SR)
    • Priority change in handling of small claims vs large claims?
    • Change in the number of claims handled by each adjuster5 at a time

Distortions

  • (Paid) CSR \(\implies\) Claims to close slower or faster in the past periods \(\implies\) Projections will be inaccurate
  • (Paid) Growing book \(\implies\) The average accident date would change over time \(\implies\) past development pattern reflects different levels of development6
  • (Paid) If no large claims in historical data, but there in the future data \(\implies\) Projections would be overestimated.7

Calendar Year effects

  • Increase in a diagonal of an AY paid losses/ earned premium can happen due to two reasons:
    • increase in the CSR
    • higher frequency of claims reported (can be confirmed with Reported claim #)

Misc.

Tricks

  • =TRANSPOSE(SORTBY(L13:O13,SEQUENCE(1,4,4,-1))) to reverse a CDF chain #spreadsheet

Aggregation

  • Problem:
    • 2012 E5 Q16 (which aggregation to choose)
  • Remember: it's all about dates…
    • Wording: (assume the change is deductible)
      • Since the change is based on policy effective dates / accident dates / claim report date \(\implies\) Use PY/AY/RY
      • Why? Since it could isolate development patterns of policies before and after the deductible
      • The bold is the kind of anomaly, you are trying to address.
    • If asked to compare AY vs RY:
      • First check the Policy Type
        • Occurrence policy \(\to\) AY
          • Involving IBNR related to claims that have not yet been reported (late reported).
        • Claims-made policy \(\to\) RY
          • Development on known claims only.
  • AY benefits
    • Many industry benchmarks are available on AY basis for comparison
    • Useful when internal or external events that impact losses are correlated to the accident dates.
  • RY benefits
    • Change in the legal and social environment which correlates more with the report date than the accident dates.
  • Quarterly vs Annual?
    • Use Annual > Quarterly
      • If company is small (not credible enough \(\implies\) unstable pattern)
      • Long term line (development pattern is long term \(\implies\) unstable in the short-run )
      • Mention both the above points together…
      • Using Quarterly data will compound the issue, and it would be more difficult to select appropriate development factors

Combine two LOBs? Product mix

  • The key point: the development factors of the mix (combined) shouldn't get affected.
  • Growth (Trend) rate should match (YoY)
  • Development pattern need not match if growth rate has matched.
  • Combine, if individually not enough data to make credible calculations.
    • ALSO, if the each of the groupings are credible enough, leave them alone.
  • Don't combine if they have different severities.
    • In general severity(long-tailed LOB)11 \(\gt\) severity(short-tailed LOB)10
  • Claim Settlement Rates (long-tailed vs short-tailed)
  • Case Reserve Adequacy: If the lines have different reserving philosophies, rept losses can have different development patterns…

  1. Think in terms of numerator and denominator. ↩

  2. Which usually mean paid losses + change in case (a single claim) reserves during the period, but the term "incurred losses" is used to refer to paid losses + change in total reserves ↩

  3. So think of it this way. Increasing case reserve adequacy (CRA) and increasing claim settlement rates (CSR) work in opposite directions when it comes to total case reserves. Increased CSR tries to reduce the total case, while CRA tries to increase the total case reserves as of a particular time period. ↩

  4. Also think of what would have happened if there was an increase in the settlement rates of larger claims.. ↩

  5. This makes sense, if you have more work load then you become less efficient and stuff… ↩

  6. E.g. 12-24 would actually be 12-25 dev factor for a growing book of business as the average date would have shifted rightwards for the second CY. ↩

  7. Inadequate case reserves. ↩

  8. Here the question specifically asked what will happen if you used paid loss developments, that is why we go for an "assumption" so that we can talk about it. ↩

  9. When asked about nothing in general, its better to be unopinionated and go for a safe bet where you are not assuming anything and just stating that there isn't enough evidence to conclude either. ↩

  10. A short-tailed LOB like auto collision is characterized by a rapid claims settlement process. For example, if a car gets into a fender-bender, the claim is typically filed, the vehicle is repaired or declared a total loss, and the claim is closed relatively quickly. The severity, while it can vary, is limited by the tangible costs of vehicle damage and immediate medical expenses. ↩

  11. In contrast, a long-tailed LOB like product liability can have much higher severity. Consider a scenario where a company manufactures a medical device that, years after its initial use, is found to cause a rare but serious health complication. The initial claim may be small, but as more patients are diagnosed with the condition and a class-action lawsuit is filed, the severity escalates dramatically. ↩

  12. If not these, then the development in the future period WILL NOT match the development in prior periods ↩

  13. We say "probably" because we are not sure about the case reserve adequacy. ↩

  14. Process of resolving a dispute through the court system ↩

  15. This paid/rept counts doesn't differentiate between small claims and large claims, it just tells us that the "Todo is checked", not whether it was a major task or a minor task. We need to look at avg paid claims and avg case o/s to fully verify whether the Todo was a heavy task (large claims) or a small one (smaller claims) ↩