1. Loss Triangle Philosophy Gary Blumsohn CARe Seminar: Cambridge, May 2008

2. Background Committee on Reinsurance Research Practical questions:  Actuaries mostly learn to do loss development on the job  Can we give guidance to improve approaches – especially on unstable triangles?

3. The Questions What types of averages do people use? Statistical tests and methods Smoothing Reversals Downward development Ignore tail-factor issue

4. Initial Attempt 12-year excerpt from RAA GL Fac Too stable! 40 responses Mean loss reserve estimate = $1.6 billion SD of loss reserve estimates = $0.2 billion CV = 13%

5. Second Attempt: Umbrella incurred loss triangle

6. Responses “Great and gutsy project!” “I believe the whole notion of "picking factors" with no statistical guidance is something of a disgrace to the profession…”

7. Responses (cont.) “While it may be helpful to share ideas on how to pick LDFs, it is vital that more information than just the triangle at hand be considered… I wouldn’t make selections without other information such as individual claim information, changes in the underlying business, comparison to competitor or industry triangles if available, etc. Of course you can’t always get the information you want……but I would hate to see people come to the seminar and learn some new selection techniques that don’t look beyond the triangle.”

10. Implied Reserves (in $millions) Mean28.0 Std. Dev8.3 Minimum10.7 2 nd lowest18.3 25 th percentile23.7 Median26.2 75 th percentile31.1 2 nd highest55.2 Maximum60.2 Mean

12. “Actuaries must not pretend to judge what they cannot scientifically model.” Leigh Halliwell Variance, Vol. 1, Issue 2, p. 216

13. Skeptic’s view of statistical methods Statistical methods measure the past You have how many data points?!! Blow-ups more likely to be from things that aren’t in the data than from 1-in-10,000 events.

14. Task Force On The Reputation Of Casualty Actuaries

15. Complete determinism: Know the future Complete determinism: Know the future Economic Perspective No determinism: Don’t know distributions No determinism: Don’t know distributions Stochastic determinism: Know the future statistically Stochastic determinism: Know the future statistically Perfect Knowledge Perfect Knowledge Risk Uncertainty Blumsohn, PCAS 1999, p. 31

16. “If you cannot measure, your knowledge is meager and unsatisfactory.” Lord Kelvin

17. The Dilemma Your knowledge is meager and unsatisfactory, but your boss needs an answer

18. Frank Knight, on the practical meaning of Kelvin’s statement for social scientists: “If you cannot measure, measure anyhow.”