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7/25/2019 Loss Aggregate 2
1/9
1
Sample Lognormal Loss RatioDistribution
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7/25/2019 Loss Aggregate 2
2/9
2
Is the resulting LR distributionreasonable?
Compare resulting distribution to historical results
Focus on level LRs, but dont completelyignore untrended ultimate
LRs
!otential "or cat or shoc# losses not captured
$ithin historical e%perience Degree to $hich trended past
e%perience is
predictive o" "uture results "or a boo#
&ctuary and under$riter should discuss the aboveissues
I" the distribution is not reasonable, ad'ust the
C(selection
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7/25/2019 Loss Aggregate 2
3/9
3
!rocess and !arameter)ncertainty
!rocess )ncertainty* Random +uctuation o" results aroundthe
e%pected value
!arameter )ncertainty* Do you really #no$ the true meano" the
loss ratio distribution "or the upcoming year? &re your trend,
loss development rate change
assumptions correct?
For this boo#, are past results a good indication o""uture
results? Changes in mi% and type o" business Changes in management
or philosophy Is the boo# gro$ing, shrin#ing or stable
Selected C( should usually be above indicated
- to ./ years o" data does not re+ect "ull range
o"possibilities
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7/25/2019 Loss Aggregate 2
4/9
4
0odeling !arameter)ncertainty* 1ne Suggestion
Select 2 e3ually li#ely e%pected loss ratios
&ssign $eight to each loss ratio so that the $eightedaverage
ties to your selected e%pected loss ratio
4%ample* 4%pected LR is 5-6, assume .72probability that true
mean LR is 5/6, .72 probability
that it is 5-6, and .72 probability that it is 8/6 Simulate the
9true: e%pected loss ratio ;re+ects
!arameter )ncertainty
