# A.5. Robertson - HG Mapping

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1. Hazard Group
Collection of WC classifications that have relatively similar expected excess loss factors over a broad range of limits.
2. Original classification methodology
• grouped 7 variables (indicative of excess loss potential) into 3 subsets based on correlation
• ran principal components analysis to determine a single representative variable
• first component was used to determine the classes
3. WCIRB classification methodology
• used 2 statistics to sort classes into HG
• first statistic = % of claims XS of \$150,00 (proxy for large loss potential)
• second statistic = difference between class loss distribution and average loss distribution
4. New classification methodology
• sorted class into HG based on their XS ratios
• note: a distribution is characterized by its excess ratios so there’s no loss of information
• used cluster analysis to group classes with similar XS ratios
• determined the optimal # of HG
• compared the new HG assignments with the prior assignments
5. Selection of loss limits - why 5 instead of the prior 17
• excess ratios at different limits are highly correlated
• there were initially too many limits below \$100,000
• 1 limit didn’t capture full variability
• matches range commonly used for retro-rating
6. Class excess ratios
• j = HG, Xi = loss for injury type i, L = limit
• Si(r) = normalized state excess ratio for injury type i = E[max(Xii - r,0)], r = L/μ
• Rj(L) = excess ratio = ∑wi,jSi(L/μi,j)
• wi,j = % loss due to injury i in group j and μi,j = average cost per case for injury i in group j
7. Credibility
• previous: z = min[n / n + k) x 1.5, 1], n = # claims in class, k = average # of claims per class
• this gave 72% of classes a credibility of 100%, which was perceived as an issue
• considered excluding medical only claims, or including only serious claims
• considered using the median rather than the mean for k, restricting k to classes with some minimal number of claims, square root method, advanced square root (by injury type)
• → no alternative was compelling enough to warrant change, so stuck with original formula
8. Steps of cluster analysis
• selection of loss limits
• metrics to evaluate cluster distances
• standardization
9. Metrics used
• Euclidian distance L2 = ‖x - y ‖2 = √∑(xi - yi)2; penalizes large deviations
• L1 = ‖x - y ‖1 = ∑|xi - yi|; minimizes relative error = PLR x |Rj(L) - Rc(L)|
10. Standardization
• applied to prevent a variable with large values from exerting undue influence on the results (each variable has a similar impact on the clusters). However:
• groups already have a common denominator (limit) which would get filtered out
• wanted to keep excess ratios between 0 and 1
• analysis didn’t produce significantly different results with or without standardization
• without it, excess ratios at lower loss limits have more influence on clusters; not undesirable since they rely on more observed values (rather than fitted distribution)
11. k-means clustering technique
• k-means groups classes into k HG so as to minimize ∑∑‖Rc - Ri22 where centroid Ri = 1/|HGi| ∑Rc is average XS ratio vector for the ith HG
• k-means algorithm: start with random clusters. Compute centroid of each cluster, and assign each class to the cluster with the closest centroid. Repeat until no class is re-assigned
• weights: to avoid letting small classes have undue influence, premium-weigh each class
12. Cooper and Milligan tests to find the best k
• Calinski and Harabasz: higher values indicates a higher between distance (B) and lower within distance (W); aka Pseudo-F test
• Cubic Clustering Criterion (CCC): compare variance explained by a given set of clusters to that of random clusters; less reliable when data is elongated (highly correlated variables), which is the case here (excess ratios correlated across limits)
13. Underwriting criteria used to modify HGs
• similarity between class codes that were in different groups
• degree of exposure to automobile accident by class
• extend heavy machinery is used in a given class
14. Comparison to old hazard groups
• new hazard groups have more even distribution of claims & premium by class
• complement of credibility was prior hazard group (many small classes stayed grouped)
• new hazard groups show less within variance and more between variance

### Card Set Information

 Author: EExam8 ID: 305202 Filename: A.5. Robertson - HG Mapping Updated: 2015-09-05 13:42:25 Tags: Robertson Hazard Group Mapping Folders: Description: Robertson NCCI 2007 Hazard Group Mapping Show Answers:

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