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Casualty Loss Reserve Seminar 2003 Session #4 Workers’ Compensation Reserving – How and when should you slice the cake?

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Casualty Loss Reserve Seminar 2003 Session #4 Workers’ Compensation Reserving – How and when should you slice the cake?. Ezra Robison, FCAS, MAAA 09/08/2003. Today’s agenda:. Failing to slice the cake Implications for triangle technology Could we generalize slicing?. Pursuing relevancy.

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Casualty Loss Reserve Seminar 2003Session #4Workers’ Compensation Reserving – How and when should you slice the cake?

Ezra Robison, FCAS, MAAA

09/08/2003

today s agenda
Today’s agenda:
  • Failing to slice the cake
  • Implications for triangle technology
  • Could we generalize slicing?
pursuing relevancy
Pursuing relevancy
  • Are actuaries pursuing increasing precision in areas of decreasing relevancy?
    • Actuarial science is forecasting
    • Slicing the cake is about forecasting
    • A better slicer is not decreasingly relevant
anecdote failing to slice the cake
Anecdote – failing to slice the cake
  • All WC
  • All the same state
  • 4 separate business units
moral of the story
Moral of the story
  • I was using one body of data to assign a tail factor to a different body of data
    • A central issue in considering “how to slice the cake”
    • Sometimes, there is no alternative
    • Sometimes, this is done unknowingly
what is the goal
What is the goal?
  • Optimize the balance between credibility and homogeneity
  • Systematize what is currently, generally, an ad hoc process
how would we optimize the balance
How would we optimize the balance?
  • Use claim, premium and exposure information at lowest reasonable level
  • Gather statistics by dimension (slices)
    • Construct relevancy statistics
    • Construct credibility statistics
    • Construct trade-off functions
  • Find the slicing that optimizes the relevancy and credibility
are these thoughts relevant to non primary carriers
Are these thoughts relevant to non-primary carriers?
  • It is not immediately obvious that those who do not own vast claim or sub-claim level detail can pursue this direction immediately
  • But valuable use of existing data will drive the development of technology throughout the industry
  • E.G. catastrophe modeling
what is relevancy
What is relevancy?
  • Based loosely on Howard Mahler’s, "An Example of Credibility and Shifting Risk Parameters," PCAS LXXVII, 1990
  • The extent to which one body of data is relevant for predicting the future of another body of data
  • Relevancy is closely tied to the concept of homogeneity
    • I like it because I find it easier to think about quantifying relevancy
how would we define relevancy
How would we define relevancy?
  • A formal definition might be based on the percent of policies (premium, exposure or expected loss cost) common to both bodies of data
  • Could also incorporate claim or sub-claim level detail (e.g. PPO savings)
how would we measure relevancy over time
How would we measure relevancy over time?
  • Trend?
    • Lower trends imply higher homogeneity
  • Average?
    • Higher averages imply higher homogeneity
  • Minimum?
    • Higher minimums imply higher homogeneity
what do we mean by credibility
What do we mean by credibility?
  • Probably not a formal definition such as Buhlmann or Classical
  • Rather, a general concept: larger bodies of data are inherently better for forecasting
what would our credibility metric be
What would our credibility metric be?
  • Number of buckets?
    • Fewer buckets implies higher credibility
  • Average size of bucket?
    • Higher average implies higher credibility
  • Minimum size of bucket?
    • Higher minimum implies higher credibility
finding the optimal combination
Finding the optimal combination
  • We may have to settle for subjectivity for now, but possible standards include:
    • Obtaining a minimum standard for each of credibility and relevance
    • Maximizing a subjectively derived measure which is a function of both credibility and relevancy
      • This is similar to maximizing the economic concept of utility
what would we gain by this approach
What would we gain by this approach?
  • Guidance in slicing the cake
  • Quality control
remaining issues
Remaining issues:
  • The subjectivity associated with finding the right balance
  • The measurement of both credibility and relevance are complicated in that they change over time
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