C.4 Special Classifications

Question 1

Challenges in determining indicated rates for

territories

Answer 1

 -Territory tends to be highly correlated with other rating
variables. As we’ve seen, this can be addressed using
multivariate analysis.
 -Territories are often set to be such small areas (e.g., zip
codes) that the data in each territory may have very limited credibility. Addressing this challenge will be the focus of this discussion.

Question 2

Two steps in territorial ratemaking

Answer 2

1. Establishing territorial boundaries

2. Determining indicated rates for each territory (preferably using a GLM due to the correlations with other variables)

Question 3

Two basic spatial smoothing approaches and

advantages of each

Answer 3

1. Distance-based: The current geographic unit’s data is
   credibility-weighted with the data from other geographic
   units, with the weights diminishing with distance. The
   advantage of this approach is that it is easy to understand and implement. The disadvantages are that it assumes that distance has the same impact for urban and rural risks, and it doesn’t consider physical boundaries (e.g., rivers, highways). This approach is suited best for weather-related perils.
2. Adjacency-based: The current geographic unit’s
   data is credibility-weighted with the data from rings
   of surrounding geographic units, with the weights
   diminishing with wider rings. This approach better
   reflects urban and rural differences, and accounts for
   physical boundaries better. This approach is suited best for socio-demographic perils (e.g., theft).

Question 4

Two categories of clustering routines (in territorial

ratemaking)

Answer 4

 -Quantile methods: Clusters will have equal numbers of
observations or equal weights.
 -Similarity methods: Clusters are based on the closeness of estimated relativities.

Question 5

Why standard ratemaking is problematic for

determining ILFs

Answer 5

 -There is generally less data for higher limits so results can be volatile.
 -Analyses can produce results that are impractical to
implement (e.g., a lower price for a higher limit).

Question 6

Assumptions commonly made in pricing ILFs

Answer 6

 -All UW expenses and profit are variable and don’t vary by limit.
 -Frequency and severity are independent.
 -Frequency is the same for all limits.

Question 7

Why loss data should be trended and developed for

ILF pricing

Answer 7

Higher limits can experience higher severity trends, and

development can take longer on larger claims.

Question 8

Limited Average Severity for a continuous

distribution

Answer 8

LAS(H) = xf(x) integrated from 0 to H + H * (f(x) integrated from H to infinity)

Question 9

What an Expense Constant accounts for

Answer 9

For expense costs that do not vary by size of risk. This is

particularly important for small policies since their expenses may be a large portion of their premium.

Question 10

Why small Work Comp risks have worse loss

experience than large risks

Answer 10

 -Small companies usually have less sophisticated safety
programs.
 -Small companies usually don’t have return-to-work
programs for injured workers.
 -Small companies are not as impacted by or do not qualify for experience rating, so they have less incentive to prevent or mitigate injuries.

Question 11

Two issues when properties are not fully insured

Answer 11

1. The insured will not be fully covered in the event of a total or near-total loss.
2. If the insurer assumes all homes are fully insured to their replacement cost when calculating rates, then the premium charged for underinsured policies will not be adequate to cover the expected losses for those policies.

Question 12

How premium rate changes as ITV increases based on

skew of severity distribution

Answer 12

 -For right-skewed distributions (small losses are more
likely), the rate per $1k of coverage will decrease at a
decreasing rate as coverage increases.
 -For uniform distributions, the rate per $1k of coverage will decrease at a constant rate as coverage increases.
 -For left-skewed distributions, the rate per $1k of coverage will decrease at an increasing rate as coverage increases.

Question 13

Coinsurance apportionment ratio, payment, and

penalty formulas

Answer 13

a = min[ F/cV , 1]
I = min[aL, F]
e = min[L, F] - I