Transcript Download Handout 2

Reserving Ranges and
Acceptable Deviations
CANE Fall 2005 Meeting
Kevin Weathers FCAS, MAAA
The Hartford
This document is designed for discussion purposes only.
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Main Discussion Points
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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
Internal Uses of Reserving Ranges
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Any internal use of the reserving product can
benefit from an understanding of the reserving
ranges (Benefit can be either explicit or implicit)
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To gauge the pricing need?
To help create next year’s operating plan?
To determine leverage for Return on Equity
purposes?
Some Approaches to the Problem
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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
The Problems of Some Approaches
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Multiple methods
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Different assumptions within each method to determine
ranges
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Range of answers represents only the range of likely
outcomes
If all methods produce the same answer – is the outcome
certain?
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?
The Problems of Some Approaches
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Mack/Bootstrapping type approaches
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Both measure the residuals of model vs. actual and use these
to develop ranges for the future payments
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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
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Some have same issue as Mack/Bootstrapping approach, but
many have an underlying model with adjustable parameters
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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?
To Build or To Buy?
Many of the concerns are obvious but important
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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
The Hartford Experiences
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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
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?
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More problems that don’t go away
when you buy software…
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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?
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Measure the modeled payouts from the models of
the two lines
Use actuarial judgment
More on correlations
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Some of the models allow ways to calculate
the correlations
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To use judgment, what must we consider?
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Seems like limited data
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?
My thoughts on correlations
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I don’t have numbers to back this up, but it seems
that three very likely drivers of payout patterns are:
1.
2.
3.
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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.
Final Thoughts
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There is much to be gained from looking at more than
the set of estimates from a handful of deterministic
methods
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The best tool in the world still needs a good craftsman
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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?