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The New NCCI Hazard Groups Greg Engl, PhD, FCAS, MAAA National Council on Compensation Insurance CASE Fall Meeting September 13, 2006. Agenda. History of previous work Methodology employed Impact of remapping. Current Hazard Groups. Assigning Classes to HGs. Prior NCCI Method
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The New NCCI Hazard Groups Greg Engl, PhD, FCAS, MAAANational Council on Compensation InsuranceCASE Fall MeetingSeptember 13, 2006
Agenda • History of previous work • Methodology employed • Impact of remapping
Assigning Classes to HGs • Prior NCCI Method • California Approach • ELF Based Method
Prior NCCI Method • Hazardousness • “Excess loss potential”
Hazardousness Variables For each state, the following seven quantities were measured by class and expressed as ratios to the corresponding statewide value: • Claim Frequency • Indemnity Pure Premium • Indemnity Severity • Medical Pure Premium • Medical Severity • Total Pure Premium • Serious Severity (including Medical)
California Methodology • Group classes with similar loss distributions together • Need to precisely define ‘similar’
1 2 3 4 5 6 7 8 9 10 CrossoverCalifornia ELF Curves
HG Remapping Rationale • What are HGs used for? • Determining ELFs
HG Remapping Approach • Makes sense to sort classes by ELF vectors • Class ELF vectors approximated by HG ELF vectors • ELF curves characterize loss distribution
HG RemappingBasic Data • For each class code, , we have a vector of ELFs: • Credibility weight with current HG ELF vector
4 Hazard Group ComparisonPercent of Premium Per Hazard Group New Mapping Current Mapping 2.5% 0.9% 5.1% 17.9% HG 1 HG 2 45.5% 39.2% HG 3 51.1% HG 4 37.8%
C A B D E F G 2 1 3 4 Hierarchical Collapsing of New Mapping
Percent of Premium MovedCurrent Mapping to New 4 Hazard Groups 80% 586 70% 60% 50% Percent of Premium 40% 219 30% 20% 10% 51 3 1 0% No Up 1 HG Down 1 HG Up 2 HGs Down 2 Movement HGs Movement * Number above bar represents the number of classes in each category.
5 6 7 8 9 3310 3213 3442 3297 3102 Number of Hazard GroupsCalinski and Harabasz Number of HGs 4 CH Statistic 2317
5 6 7 8 9 110 108 112 111 125 Number of Hazard GroupsCubic Clustering Criterion Number of HGs 4 CCC Statistic 89
Number of Hazard Groups Calinski and Harabasz Number of HGs All Classes 50% Credibility Classes Full Credibility Classes 4 2317 793 433 5 3310 759 393 6 3213 705 450 3442 1025 638 7 8 3297 958 620 9 3102 915 584 Cubic Clustering Criterion Number of HGs All Classes 50% Credibility Classes Full Credibility Classes 4 89 51 37 5 110 50 34 6 108 48 36 59 42 7 112 8 111 57 41 125 9 56 40
Three Key Ideas • Map based on ELFs • Compute ELFs by class • Cluster Analysis
HG RemappingObjective Break C = set of all class codes, into Hazard Groups:
HG RemappingBasic Data For each class code, , we have a vector of ELFs:
Using Hazard Groups • (HG mean) • approx by for • Want as close as possible to
HG Remapping Methodk-means Splits classes into HGs to minimize
Optimal HGs • % of total variance explained • Analogous to an R-squared • k-means maximizes this
Optimal HGs • Want well separated, homogeneous HGs • Minimize within variance • Maximize between variance
Optimal HGs • Between variance vs. within variance • Have one variance for each variable (ELFs at different attachment points) • Need to consider variance-covariance matrices
Optimal HGs Dispersion matrix of whole data set is given by
Optimal HGs Dispersion matrix of HGi is given by
Optimal HGs • If we let • Then
Optimal HGs • Pooled within group dispersion matrix • Weighted between group dispersion matrix
Optimal HGs • Between variance vs. within variance • T = B + W • k-means minimizes trace W