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


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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 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

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


A brief history of technology and triangles

A brief history of technology and triangles


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)


Relevancy

Relevancy


A graphical representation

A graphical representation


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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