Casualty Loss Reserve Seminar

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Casualty Loss Reserve Seminar

• Call Paper Program
• Loss Reserving without Loss Development Patterns
  - Beyond Berquist Sherman

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We used a few simplifications to keep this
understandable

• We made up the data
• We select development factors based on the volume
  weighted average of the last three diagonals
• We tried to keep to a minimum the number of
  slides with lots of numbers that are hard to read

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The data is constructed to allow for variations
in reporting and payment patterns

• Ultimate losses based on hypothetical frequency
  and severity assumptions
• Annual trend of 5 per year
• 1 frequency
• 4 severity
• We include ten years in the data
• Ten year total ultimate losses of 766.5 million
• Hypothetical development patterns applied to the
  hypothetical ultimates to derive loss development
  data
• Variation in the patterns used to create
  hypothetical scenarios

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We derived four scenarios to test the accuracy of
various reserving techniques

• Scenario 1 (Base Scenario) - Stable settlement
  and reserving patterns
• Scenario 2 - Case reserve strengthening
• Assumes about six months acceleration in
  reporting pattern
• Scenario 3 - Settlement rate acceleration
• Assumes about six month acceleration in claim
  settlement and loss payment patterns
• Scenario 4 - Case reserve strengthening and
  settlement rate acceleration
• Assumes about six month acceleration in reporting
  and payment patterns

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The loss reporting and payment patterns
underlying the base scenario are as follows
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In a stable environment, loss reserving is easy.
An incurred loss triangle might look like this ...
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and a paid triangle might look like this ...
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and simple projections all give the same result
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Introducing changes to the settlement and case
reserving patterns expose weaknesses in
traditional loss development analyses

• Scenario 2 - Case Reserve Strengthening
• Traditional loss development factor (LDF)
  projection based on incurred data will
  underestimate the amount of strengthening
• This results in over-projection of ultimate
  losses
• Ten year total projection is 796.0 million
• 29.5 million higher than the actual ultimates of
  766.5 million

The misestimate for 12 months alone causes the
projected ultimates to be too high by 17.8
(111.4 m vs 94.5 m)
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Changes in the settlement rate and payment
patterns can be even more significant of a
distortion

• Scenario 3 - Settlement Rate Acceleration
• Traditional LDF projection using paid losses
  results in over-projection of ultimate losses
• Ten year total projection is 840.7 million
• 74.2 million higher than the actual ultimates of
  766.5 million

This error causes a 38 over-projection on the
latest year (130.8 m vs 94.5 m)
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Loss reserving in a changing claim settlement or
case reserving environment requires advanced
techniques, and significant judgment

• Berquist-Sherman (PCAS LXIV, p123)
• Judgmental adjustments to prior diagonals to
  approximate the settlement rate and or case
  reserve levels on the current diagonal

Adjusted Loss Development Factors
Adjusted
Actual

• Adjusted loss development pattern applied to
  the unadjusted (actual) data

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The techniques in this call paper adjust the
latest diagonal instead of the prior data

• Ultimate Closed Claim Severity Technique
• Projects ultimate losses using traditional
  methods
• Calculates implied unpaid loss triangle
• Repeat this approach for claims to get estimated
  unclosed claims triangle
• Ratio of the unpaid loss triangle to unclosed
  claim triangle gives the estimated unclosed claim
  severity triangle

Estimated Unpaid
Projected Ultimates
Paid to Date
minus
equals
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The unclosed claim severity triangle is used to
estimate the latest diagonal severities
consistent with the historical data
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When there are changes in patterns, this method
replaces the distorted latest diagonal with an
adjusted diagonal consistent with prior periods
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The second new technique in this paper does not
use loss development factors for any year

• Incremental Closed Claim Severity Method
• Calculates incremental paid losses and closed
  claims for each year between evaluation points
• Calculates incremental closed claim severity
  triangle
• The historical incremental closed claim
  severities are used to estimate future
  incremental severities
• Historical closed claim data is used to estimate
  future incremental closed claims

Increm. Closed Claims Severity
Increm. Paid Losses
Increm. Closed Claims
divided by
equals
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The sumproduct of severities and closed claims
below the diagonal provides an estimate of the
remaining closed claim severities by year
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When there are changes in patterns, this method
mostly avoids the distorted diagonals
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These severities are used to estimate ultimate
losses
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In summary, the new methods provide significant
improvement in projection accuracy

• As with all techniques, they produce the correct
  result in a stable environment
• With changes in case reserve adequacy and/or
  settlement rates, they are much more accurate

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All methods work when life is stable and
predictable
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But the adjusted methods are more accurate when
things are changing
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These new techniques do not necessarily produce a
better adjustment than the traditional advanced
techniques. However...

• They may be more understandable to company
  management
• They allow explicit reflection of known changes
  in mix of business or other factors that affect
  trend
• They allow easy combination of case reserve and
  settlement rate adjustments
• They work equally well with calendar year changes
  and accident year changes
• They reflect recent claim frequency experience
• They provide reasonableness testing for more
  traditional methods

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We used many simplified approaches and
assumptions. Refinements are possible

• Use unpaid claim severities instead of unclosed
• More sophisticated forecasting techniques
• Blending with post-change experience
• Reasonableness testing
• implied loss ratios, severities, pure premiums
• Sensitivity testing