Siewert

Question 1

General approaches to evaluate excess ult. loss

Answer 1

Loss Ratio Approach
Implied Development Approach
Direct Development Approach
BF approach

Question 2

Loss Ratio Approach when to use

Answer 2

When no data is available
Use for immature years where data is sparse

Question 3

Loss Ratio Approach steps

Answer 3

get per occ excess losses
get per agg excess losses
add together above two

Question 4

Pros and Cons for Loss Ratio Approach

Answer 4

Advantages -
can be used when no data is available or data is immature
loss ratio estimates can be consistently tied to pricing programs
relies on a more credible pool of company and industry experience

Disadvantages -
Ignores actual emerging experience
May not properly reflect account characteristics, since development may emerge differently due to the exposure written

Question 5

Implied development approach steps

Answer 5

• develop full coverage losses to ult
• develop ded losses to ult
• ult xs loss = ult GU - ult capped

need to index different limits for inflation to keep ded/excess level year-to-year

Question 6

Benefits of high deductible programs

Answer 6

• Price flexibility with additional risk passed to larger insureds
• Improved residual market charges and premium taxes in some states
• Realizing cash flow advantages (similar to those of paid loss retro policies)
• Provides insureds a way to control losses while protecting against random, large losses
• Allows “Self-Insurance” without having insured submitted to sometimes demanding state requirements

Question 7

How to estimate the overall reserve while reflecting differing mixes of deductibles and limits

Answer 7

After selecting appropriate development factors, apply them at the account level using each account’s deductible & limits

Then aggregate the estimated ultimate over all accounts

Question 8

Selecting the Loss Ratio for the Loss Ratio Method

Answer 8

• Use the company experience by state and calculate the full-coverage loss ratio using an individual account’s premium distribution by state
• We might blend that experience with industry experience with credibility

Note: Loss experience should be developed to ultimate, brought on level and trended to the appropriate exposure period for calculating loss ratios

Question 9

Loss Ratio Method:
Estimate of per-occurrence excess losses

Answer 9

Question 10

Loss Ratio Method:
Estimating the aggregate loss charge

Answer 10

Question 11

Loss Ratio Method:
Advantages and Disasvantages

Answer 11

Advantages
- Useful when no data is available or data is very immature
- Loss ratio estimates can be consistently tied to pricing, initially
- Relies on a more credible pool of company and/or industry experience

Disadvantages
- Ignores emerging experience
—> Not very useful after several years of development
- May not properly reflect account characteristics and losses may develop differently due to type of exposure written

Question 12

Implied Development Method

Answer 12

• Unlimited loss tail factor should be consistent (higher) with limited tail
• Limited LDFs must be calculated to reflect inflation-indexed limits at different accident years

Question 13

Implied Development Method:
Indexed LDFs

Answer 13

To calculate limited LDFs for deductible loss, index limits for inflation:
- This keeps the proportion of deductible/excess losses constant around the limit from year to year
- Otherwise, a constant deductible implies increasing excess losses

Possible ways to determine the index:
Fit a line to average severities over the long-term history
Use an index that reflects the change in annual severity

Question 14

Implied Development: Advantages and Disadvantages

Answer 14

Advantages
Provides an estimate for excess losses at early maturities, even when excess losses haven’t emerged
LDFs for limited losses are more stable than LDFs for excess losses

Disadvantages
Misplaced focus, because we would like to explicitly recognize excess loss development

Question 15

Direct Development Method

Answer 15

Given limited and full coverage LDFs, there are XSLDFs that balance limited and excess development with full coverage development.

Disadvantages:
XSLDFs can be quite leveraged and volatile, therefore difficult to select
If no excess losses have emerged, we can’t estimate ultimate

Question 16

Credibility-Weighted Method formula

Answer 16

Question 17

Credibility weighted method: Advantages and Disadvantages

Answer 17

Advantages:
Ties with pricing estimates for inmature years where excess losses haven’t emerges
Estimates are more stable over time compared to direct development

Disadvantages:
Ignores actual experience for the complement of credibility
—> might use alternative credibility weights that are more responsive to actual experience if desired

Question 18

Limited Severity Relativity

Answer 18

Ratio between limited and unlimited severity

Question 19

Relationship between limited LDF, unlimited LDF, and severity relativities

Answer 19

C = counts
S = severity
R = severity relativity
t = age
L = limit

Question 20

Relationship between XSLDF, unlimited LDF, and severity relativities

Answer 20

Question 21

Relationship between Limited, XS, and unlimited LDFs

Answer 21

Question 22

Relationships between limited severity relativities over time

Answer 22

Severity relativity should decrease as age increase
-> more losses are capped at per-occurrence limits as age increase

Severity relativity should be higher for higher limits (and fall more slowly)
-> a higher limit means less of the loss is capped, so the relativity is high

Question 23

Distributional Model

Answer 23

Fit a model (e.g. Weibull) to severities in order to calculate consistent relativities and LDFs
-> this makes it easier to interpolate among limits and years

Distribution parameters vary over time by development period
-> Parameters can be estimated by minimizing chi-sq between actual and fitted severity relativities at deductible size
-> Constrain parameters so that the model produces the actual unlimited severity at maturity

Question 24

Partitioning expected development around the deductible limit

Answer 24

Question 25

Relationship of excess and limited development over time

Answer 25

As development increases, an increasing portion of development is excess the deductible

Question 26

Aggregate Loss Limit

Answer 26

Limits the total loss below the deductible that are paid by the insured

Question 27

Collective Risk Model approach to Aggregate Limits

Answer 27

Model Freq and Sev separately
–> Siewert uses Weibull for severity and Poisson for claim counts
Combined freq and sev into a collective risk model
Sample from collective risk model to calculate development factors
–> Might improve by including parameter risk in the model
Use the BF method with LDF from model to estimate the losses in excess to the aggregate limit

Question 28

Relationship regarding development of losses excess of aggregate limits

Answer 28

Development for losses decrease more rapidly over time with smaller deductibles than larger ones
-> because most later developments is in layers above to the limits

Development is more leveraged for larger aggregate limits
-> Takes longer for losses to breach the limits

Question 29

BF method for aggregate limits

Answer 29

Question 30

Service Revenue

Answer 30

Revenue for an insurer to service a claim under high ded program

Question 31

Service Revenue Asset Formulas

Answer 31

Question 32

Ways to handle allocated claims expense for high deductible programs

Answer 32

Account manages the expense
–> Development pattern should be loss-only

Treated as loss and subject to limit
–> should use loss+ALAE for development patterns

Question 33

Entry Ratio formula

Answer 33

Aggregate Limit / Limited Loss under ded limit

Question 34

charge formula

Answer 34

aka. Excess ratio, = 1 - Limited Severity/E[Unlimited Sev @Ult]

Question 35

Implied Development Method

Answer 35

• Unlimited tail factor should be consistently higher than limited tail
• Limited LDFs must be calculated to reflect inflation indexed-limits at different AY