C&V - multidimensional cred for class freq

Question 1

why ELFs published by NCCI are difficult to estimate

Answer 1

because losses are driven by small # of very large claims

Question 2

Couret & Venter partially address the pricing difficulty (of estimating ELFs) by observing that

Answer 2

since the physical circumstances are similar for significant injury types, claim frequency between those injury types are correlated

they use those correlations to gain additional information in estimating credibility weighted claim frequencies by injury type

NCCI estimates excess ratios for each injury type separately, and does not use information about correlations between injury types

Question 3

Couret & Venter use correlations between different injury types to

Answer 3

build a model based on less-severe injuries for which more data exists

Question 4

frequency and severity trends of injury types

Answer 4

• frequency of injury types generally decreases as you move down list
• severity generally increases as you move down with exception of PT usually being more severe than F

Question 5

C&V take ratios of

Answer 5

claim counts for each injury type to TT injury type for every class code

-effectively they look at each TT claim as an exposure that could produce a more severe claim

Question 6

C&V assume that variance of ratios

Answer 6

decreases as mi increases

mi=#TT claims in class code i

Question 7

C&V seek to find credibility-weighted versions of Vi, Wi, Xi, Yi as

Answer 7

estimates of population means which are denoted as vi, wi, xi, yi

-procedure will seek to find credibility factors b, c, d, e that will vary by injury type and class

Question 8

as a result of credibility procedure, can get different estimates of

Answer 8

expected claim frequency by injury type for particular class in HG compared to claim frequency for HG as whole

Question 9

can use these class-level expected claim frequencies to get

Answer 9

class-level ELFs which can be used to more precisely rate a risk in given class compared to using NCCI ELFs at larger HG level

Question 10

after C&V perform credibility procedure, tested results of analysis to see if their procedure produces improvement in estimating injury type ratios by class compared to using the same ratios for all classes within HG

Answer 10

• split data into 2 parts: sample for analysis (even years) and holdout sample (odd years)
• in subsequent tests performed, try best to predict injury type ratios for holdout sample results using data from analysis
• injury type ratios for holdout sample calculated just like raw Vi ratios for sample used in analysis
• C&V compare 3 possible methods of determining injury type ratios in their ability to predict injury type ratios for holdout sample:

Question 11

C&V compare 3 possible methods of determining injury type ratios in their ability to predict injury type ratios for holdout sample:

Answer 11

1. HG injury type ratios (ie Vh)
2. raw sample data injury type ratios (ie Vi)
3. injury type ratios resulting from credibility procedure (ie vi^est)

Question 12

2 tests used by C&V to see if their procedure produces improvement in estimating injury type ratios by class compared to using the same ratios for all classes within HG

Answer 12

initial sum of squared errors test

quintiles test

Question 13

C&V attribute credibility procedure performs best but doesn’t show much of an improvement over using HG ratios to

Answer 13

1. estimators derived from data are designed to fit that data (but you wouldn’t change this since whole point of estimating is to apply results to new data sets)
2. class data by year is volatile
   - C&V note that this test masks the true improvement generated by using credibility procedure and decide to use an additional test to show this

Question 14

Quintiles Test

Answer 14

• procedure for Quintiles Test which is done for each combo of injury type and HG:
  1. sort injury type relativities produced by credibility procedure for all classes in increasing order (ie vi^est); will use these to classify classes into quintiles
  2. group classes into quintiles based on sorted relativities; size of quintiles should be set such that each quintile has about the same #TT claims;
  3. calculate the weighted average injury type relativity across all classes within each quintile and within HG; do this step for each of 3 methods and for holdout sample using their respective relativities
  4. use results from step 4 to calculate the SSE for each of 3 methods

SSE =(step3 rel to quintile/step3 rel to HG - step3 holdout rel to quintile/step 3 holdout rel to HG)^2

5. method that produces lowest SSE is deemed best for that particular injury type and all classes in that HG;

Question 15

using initial sum of squared errors test, what procedure is best

Answer 15

credibility procedure performs best but doesn’t show much of an improvement over using HG ratios

Question 16

quintiles test shows

Answer 16

that their credibility procedure yields a substantial reduction in SSE when compared to other methods (really, this just means that using quintile injury type ratios is more accurate than HG level ratios but not necessarily that procedure is appropriate for class-level estimation)

-their procedure doesn’t show an improvement for HG A

Question 17

reason C&V claim that their procedure doesn’t show an improvement for HG A

Answer 17

due to classes in HG A being very homogeneous so wouldn’t expect injury type ratios to vary much within HG

Question 18

idea of multi-dimensional credibility

Answer 18

is to take advantage of extra claim frequency info for a class instead of simply relying on HG average; this result in more accurate predictions of claim frequency for class

Question 19

claim counts between different injury types are correlated; if class has higher freq of major and minor claims relative to HG average

Answer 19

it probably has higher freq of F and PT claims

Question 20

purpose of holdout sample

Answer 20

A holdout sample is a split of the original dataset that was not used to build the model and is instead used for testing the predictive power of the model.

If the model does not do a good job of predicting the holdout sample results, it is likely that the model has been overfit to the sample data used in building the model (or that the model has poor predictive power in general).

Question 21

2 ways of producing an unbiased Holdout Sample from a dataset with multiple years of data.

Answer 21

1. use even years in the model and odd years as the holdout sample. This will make sure both datasets are equally impacted by seasonality or trends over time.
2. Another option would be to select risks at random and assign them to the model building data or the holdout sample based on a random number generator.

Question 22

multi-dimensional credibility technique: Homogeneity

Answer 22

multi-dimensional will result in excess ratios by class, instead of
excess ratios by hazard group (a group of classes).

The risks within a class will be more homogeneous than the risks within a group of classes.

Question 23

multi-dimensional credibility technique: Credibility

Answer 23

both improves and worsens credibility of excess
ratio estimates, in different ways.

Credibility is improved because excess ratios for each injury
type are calculated using data from other correlated injury types, so more information and credibility goes into the estimates.

Credibility is worsened because the same data is subdivided
much more finely by class instead of by hazard group, so the sample size that each excess ratio is based off of is much smaller.

Question 24

multi-dimensional credibility technique: Predictive Stability

Answer 24

both improves and worsens predictive stability, in
different ways.

Predictive stability is improved because data from more common minor injury
types is included and these claims are more stable from year-to-year than the less frequent major injury types.

Predictive stability is worsened because class level data is used, and the
claims for each class will be more volatile from year-to-year than the claims at the hazard group level.