Fisher Retro2

Question 1

when per occurrence limit is applicable,

Answer 1

table M distributions will no longer be appropriate as they don’t recognize overlap between occurrence limit and aggregate limit

Question 2

occurrence limit reduces

Answer 2

the variance of aggregate loss distribution; this is because variance of underlying severity distribution is reduced by occurrence limit

-in general, the smaller the limit, the less variance in severity distribution, so limited aggregate distribution will have less variance as well

Question 3

have 2 options for how to deal with estimating excess losses with per occurrence limit

Answer 3

1. can estimate per occurrence excess loss separately from limited aggregate excess loss; obtain expected limited aggregate excess loss using a limited table M which is identical to table M built using limited loss data instead of unlimited loss data
2. can estimate per occurrence excess losses and limited aggregate excess losses simultaneously; can obtain these amounts using a table L where table L charge will include charge for both per occurrence expected excess losses as well as limited aggregate excess losses

Question 4

limited table M

Answer 4

• is the same as creating a regular table M but you use limited losses for each policy instead of unlimited losses and a separate table is built for each occurrence limit
• diagram looks the same except now vertical axis represents limited losses or limited entry ratios
• all same methods for calculating the areas can be used and properties of tables are basically identical

Question 5

since presence of occurrence limit would normally require entirely new tables (varying by occurrence limit) compared to table M, approximation can be used to simulate limited table M by

Answer 5

adjusting column used from a regular table M

can use insurance charge reflecting loss limitation procedure

Question 6

insurance charge reflecting loss limitation procedure

Answer 6

• use procedure to change table M column used for risk with occurrence limit to be column that normally be used by larger risk in absence of occurrence limit
• to perform, add an extra term called loss group adjustment factor into calculation of adjusted expected loss for risk
• if you use procedure, you are still simulating a limited table M, you will use limited table M balance equations instead of regular table M balance equations to perform your table M search

Question 7

thinking behind insurance charge reflecting loss limitation procedure

Answer 7

occurrence limit reduces the variance of limited aggregate loss distribution compared to unlimited aggregate loss distribution which is the same thing that occurs as we move to larger risk sizes

Question 8

how NCCI’s Insurance Charge Reflecting Loss Limitation procedure reflects the
selection of a loss limitation on a retrospectively rated policy.

Answer 8

NCCI uses the ICRLL procedure to shift the Table M column used to that of a larger risk as an approximation to using a Limited Table M.

This is done by adjusting the expected losses of the risk used to lookup the expected loss group (Table M column) by an adjustment factor

Question 9

table L charge includes

Answer 9

charge for per occurrence limit in addition to charge for aggregate limit

so creating is slightly different from table M and limite table M

Question 10

separate table L would be built for

Answer 10

each occurrence limit

Question 11

table L entry ratios, charge, and savings

Answer 11

will be actual limited losses divided by expected unlimited losses

table L charge: average difference between risk’s actual unlimited loss and actual limited loss + risk’s expected % of limited losses excess of rE[A]

table L savings: average amount by which risk’s actual limited loss falls short of rE[A]

Question 12

Table L Charges and Risk Size

Answer 12

• as risk size goes to infinity, variance in entry ratio goes to 0 and curves will flatter
• graph is similar to Table M graph but asymptote is different

Question 13

table L differs from table M

Answer 13

Table L incorporates a per accident limit and accounts for the overlap between the charge for accident limit and the charge for the aggregate limit, whereas Table M only reflects the charge for the aggregate limit.

Question 14

final premium for a retrospectively-rated workers compensation policy compared to a large deductible workers compensation policy.

Answer 14

final premium for a retrospectively-rated workers compensation policy is typically greater than for a large deductible workers compensation policy.

Retrospectively rated policies provide coverage for ground-up losses, even if there are limits on the amount of actual losses used in premium calculation.

LDD policies provide coverage in excess of the deductible(s), so the premium will be lower, since much less coverage is provided.

Question 15

If the aggregate loss limits are set too low (based on incorrect expected losses), then

Answer 15

then there is a higher probability of losses exceeding these limits, and there should be an additional charge for this.

The loss component of the policies will be priced as expected losses in excess of the per occurrence limit + expected limited losses × limited table M insurance charge. If the expected losses are too low, then both expected excess losses and expected limited losses will be too low, and the policies will be under-priced.

Question 16

how the impact of the estimation error (expected losses 20% too low) on per occurrence excess loss adequacy varies between smaller and larger sized risks.

Answer 16

The per occurrence charges would be 20% too low for all risk sizes if based on expected ground-up losses that were 20% too low (and we assume the XS ratios don’t change). In dollar terms this will be larger for larger risks.

Question 17

overlap in a retrospective rating plan with a maximum
premium and per-accident limit.

Answer 17

The overlap reflects that the presence of a per-accident limit makes it less likely that the aggregate amount of losses that correspond with the maximum premium will be hit with limited losses.

Question 18

how the NCCI Retrospective Rating Plan accounts for the maximum premium,
per-accident limit, and overlap.

Answer 18

NCCI uses the ICRLL procedure to shift the expected loss group to a bigger size to
approximate the effect of a per-accident limit on aggregate losses.

i. Obtain the excess ratio for the occurrence limit from NCCI tables.
ii. Calculate the Adjusted Expected Loss as the unlimited expected losses times the
state/hazard group adjustment factor times the loss group adjustment factor.
iii. Lookup the Expected Loss Group based on the Adjusted Expected Loss.
iv. Lookup the Table M charge for the Expected Loss Group, with the entry ratio being the aggregate loss limit divided by expected limited losses. This will be the aggregate charge for limited losses, and will approximate the charge derived from a Limited Table M.

Question 19

how a Table L accounts for the maximum premium, per-accident limit, and overlap.

Answer 19

Table L is based on limited loss data and varies by per-accident limit, so there will be no overlap when looking at aggregate charges. The Table L charge includes the charge for both the per-accident limit and the maximum premium (aggregate limit).

Question 20

entry ratio curve - Table L

Answer 20

y=A_D/E[A];

area under limited loss curve = 1-k

k=excess ratio due to per occurrence limit=1-E[A_D]/E[A]

φ_D*(r) = area between horizontal line r and limited loss + k

φ_D*(0) = 1, φ_D*(inf) = k

ψ_D*(r) = area between limited loss and horizontal line r

ψ_D*(0) = 0, ψ_D*(inf) = inf

area from (0,0) to (1,r) = r

r=ψ_D*(r) + 1 - φ_D*(r)

Question 21

explain what the ICRLL procedure does, and what it is meant to approximate

Answer 21

The ICRLL procedure is used to simulate using a Limited Loss Table M by using a standard TableMwithaformulaadjustment. TheformulaadjustmentisthattheExpectedLossesusedin determining the Expected Loss Group are multiplied by a State/Hazard Group relativity and a Loss Group Adjustment Factor. This results in shifting the Expected Loss Group to a different group, which results in a charge more closely resembling the charge derived from a Limited Loss Table M.