1. 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

2. 2 Today’s agenda: Failing to slice the cake Implications for triangle technology Could we generalize slicing?

3. 3 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

4. 4 Anecdote – failing to slice the cake All WC All the same state 4 separate business units

5. 5 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

6. 6 A brief history of technology and triangles 1970sBerquist & Sherman, Fisher & Lange Making the most out of triangles 1990sImproved hardware and retrieval software Easier to retrieve triangles TodayImproved database managers Easier to drill down Future?Can we better leverage the detail we collect?

7. 7 What is the goal? Optimize the balance between credibility and homogeneity Systematize what is currently, generally, an ad hoc process

8. 8 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

9. 9 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

10. 10 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

11. 11 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)

12. 12 Relevancy PY  122436486072 19970.3505001,1001,250 19980.4005501,2001,300 19990.8806101,3501,4001,600 20000.9106701,4501,550 20010.9507201,600 20021.000800

13. 13 A graphical representation

14. 14 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

15. 15 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

16. 16 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

17. 17 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

18. 18 What would we gain by this approach? Guidance in slicing the cake Quality control

19. 19 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