Reserving Ranges and Acceptable Deviations

1. Reserving Ranges and Acceptable Deviations CANE Fall 2005 Meeting Kevin Weathers FCAS, MAAA The Hartford This document is designed for discussion purposes only.

2. Main Discussion Points • Some internal uses of a Range of Reserves concept • Some approaches to the problem • The problem with some approaches • Considerations for Building vs. Buying • Questions that don’t go away when you buy software

3. Internal Uses of Reserving Ranges • Any internal use of the reserving product can benefit from an understanding of the reserving ranges (Benefit can be either explicit or implicit) • To gauge the pricing need? • To help create next year’s operating plan? • To determine leverage for Return on Equity purposes?

4. Some Approaches to the Problem • Multiple methods – range of answers represents the range of outcomes • Different assumptions within each method to determine ranges (varying some parameter) - then use these to determine a range • Mack/Simulation type approaches • Statistical approaches

5. The Problems of Some Approaches • Multiple methods • Range of answers represents only the range of likely outcomes • If all methods produce the same answer – is the outcome certain? • Different assumptions within each method to determine ranges • Many methods don’t have easily adjustable parameters • What are the probabilities of each input? • Do I need to determine a distribution of the parameter that I plan to vary to generate the reserve distribution?

6. The Problems of Some Approaches • Mack/Bootstrapping type approaches • Both measure the residuals of model vs. actual and use these to develop ranges for the future payments • Is this history sufficient to determine the possible future deviations from expected? • Is it clear how to adjust for known/projected changes in the environment? (Example: assumptions about future inflation) • Statistical approaches • Some have same issue as Mack/Bootstrapping approach, but many have an underlying model with adjustable parameters • There is a cost associated with complexity… can you explain the method you used to get an answer to the party that requested the answer?

7. To Build or To Buy? Many of the concerns are obvious but important • What model/approach do you desire? • Do you have the skill required to build this model? (Actuarial, Programming, Statistical) • Do you have the resources (time) to build and maintain the model? • Is the model readily available to be purchased? • What requirements do you have for the model? • Consider extras in the software

8. The Hartford Experiences • We want to add a statistical method to compliment the deterministic work we are doing • As the models became more sophisticated, they became harder to justify building ourselves - yet also harder to find available for purchase • We wanted outputs of the model to be useable for other applications (this is more of a connectivity issue) • We knew that no software would eliminate all difficulties, and that some of the remaining issues might be difficult

9. Questions that don’t go away when you buy software… Do we really understand the model? Do we really understand the default choices that the software makes when building the model? Is the available data large enough to contain: • All the relevant variation for forecasting • The full time period for the payments (can it reasonably calculate a “tail”?) If not, how can this be approximated and added to the model?

10. More problems that don’t go away when you buy software… • Once you have answered the previously named questions, you have to consider how to combine ranges for multiple lines… how do you do this? • One answer – use correlations and a copula • Where do we get these correlations? • Measure the modeled payouts from the models of the two lines • Use actuarial judgment

11. More on correlations • Some of the models allow ways to calculate the correlations • Seems like limited data • To use judgment, what must we consider? • That we are trying to determine the correlation of the loss payouts, not the loss ratios • What would drive the loss payments to the high or low end of a reserve range? Are these things related in the lines I am looking at?

12. My thoughts on correlations • I don’t have numbers to back this up, but it seems that three very likely drivers of payout patterns are: • Changes in the claim department’s practice • Changes in the legal environment • Changes in the inflation rate • All three of these would cause high correlations for long tailed lines… not diversification effects.

13. Final Thoughts • There is much to be gained from looking at more than the set of estimates from a handful of deterministic methods • The best tool in the world still needs a good craftsman • If you were asked tomorrow to determine a range around the reserves, would you be ready to begin the work, and would you know what to consider?