Actuarial Notes

CAS Exam 8 Fall 2012, Question 5

Study guide: Exam 8

The following data is used to price an excess of loss workers compensation policy:

  • Data is available for the following injury types: fatal, permanent total injury (PT), major permanent partial (Major), minor permanent partial (Minor), temporary total (TT), and medical-only (Med).
  • A multi-dimensional credibility technique (predicted) was used to estimate the frequency for class 5160.
  • Class 5160 is in hazard group F.
Hazard Group F Fatal PT Major Minor TT Med
Frequency Relativity to TT 0.006 0.006 0.085 0.37 1.00 3.6
Severity Relativity to TT 80 100 30 4 1.00 0.3
Loss Elimination Ratio at $250,000 27% 22% 57% 100% 100% 100%
TT Frequency per $100 payroll 0.0002
TT Severity for Hazard Group F $10,000
Hazard Group F for Fatal Claims Predicted Raw Data Holdout Sample
Quintile 1 0.75 0.70 0.90
Quintile 2 0.90 0.90 0.95
Quintile 3 1.00 1.00 1.00
Quintile 4 1.10 1.10 1.05
Quintile 5 1.25 1.30 1.10
Mean 1.00 1.00 1.00
Hazard Group F for PT Claims Predicted Raw Data Holdout Sample
Quintile 1 0.70 0.75 0.80
Quintile 2 0.90 0.90 0.90
Quintile 3 1.00 1.00 1.00
Quintile 4 1.15 1.20 1.10
Quintile 5 1.20 1.25 1.20
Mean 1.00 1.00 1.00
  • The hazard group relativities for Major, Minor, TT, and Med will be used.
  • The multi-dimensional credibility relativities for PT claims will be used.
  • Class 5160 is in Quintile 4 for both Fatal and PT claims.

Part a (1.25 points)

Determine whether multi-dimensional credibility relativities should be used to estimate the expected loss for fatal claims.

Part b (1.75 points)

Based on part a. above, calculate the expected loss for an excess of $250,000 workers compensation policy with $10 million in payroll.

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