A.6. Couret & Venter - WC Credibility

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A.6. Couret & Venter - WC Credibility
2015-09-05 11:40:34
Couret Venter WC Credibility

Couret & Venter - Using Multi-Dimensional Credibility to Estimate Class Frequency in Work Comp
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  1. Types of injuries
    • fatal (F)
    • permanent / temporary total injury (PT / TT)
    • major / minor permanent partial impairment (major / minor)
    • temporary total (TT)
    • medical-only (med)
  2. Development of the credibility procedure
    • serious injury types have low frequency and therefore unstable claim counts
    • however they're correlated (caused by similar events) so this can be used to derive credibility
    • Robertson didn't use information about correlation between injury types
  3. 3 methods to estimate injury type ratios for a class
    • hazard group injury type ratio (Vh)
    • raw sample data injury type ratio (Vi)
    • injury type ratio from credibility procedure (vest)
  4. Holdout sample
    • split dataset in 2 parts w/o bias (paper uses odd & even years; could use random selection)
    • build model on 1 part of the data
    • test model predictions on other part of data
  5. Multi-dimensional credibility procedure
    • create holdout sample
    • want to get credibility-weighted ratios viest where instead of just using one credibility z and the same-type complement by hazard group, they use multiple injury types and compare each class level ratio by injury type to the hazard ratio for that injury type
    • single: viest = ZVi + (1 - Z)Vh = Vh + Z(Vi - Vh)
    • multi: viest = Vh + b(Vi - Vh) + c(Wi - Wh) + d(Xi - Xh) + e(Yi - Yh)
  6. Expected excess losses at limit L for class i for Fatal claims
    • (Payrolli/100) * (FreqTT,i) * (SevTT,i) * (viest) * (SevRelV,i) * [1 - LERV,i(L)]
    • then sum across all injury types to get total expected excess losses
  7. SSE Test
    • SSE = ∑(V* - Vholdout)2 → credibility procedure works best but barely:
    • estimators from even years data designed for that data
    • class data by year is volatile
    • HG A specifically has very homogeneous classes, so injury type ratio doesn't vary much
  8. Quintiles Test
    • sort all relativities in increasing order
    • group classes into 5 groups based on sorted relativities with ≈ same # of TT claims
    • calculate average by class in each quintile and divide by injury type relativity for the HG
    • calculate SSE for each method as SSE = ∑(V*/Vh - Vholdout,quintile/Vholdout)2
    • substantial reduction in SSE in new method (except class A deemed homogeneous)