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

1. Casualty Loss Reserve Seminar 2003Session #4Workers’ Compensation Reserving – How and when should you slice the cake? Ezra Robison, FCAS, MAAA 09/08/2003

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

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

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. A brief history of technology and triangles

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

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. 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. 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. 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. Relevancy

13. A graphical representation

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

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