Siewert

Question 1

Benefits of high deductible programs

Answer 1

• Price flexibility with additional risk passed to larger insureds
• Improved residual market charges and premium taxes in some states
• 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 for easier “self-insurance” for insureds

Question 2

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

Answer 2

After selecting appropriate development factors, apply them at the account
level using each account’s deductibles & limits.
Then aggregate the estimated ultimate over all accounts.

Question 3

Selecting the Loss Ratio for the Loss Ratio Method

Answer 3

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

Question 4

Loss Ratio Method:
Estimate of per-occurrence excess losses

Answer 4

Question 5

Loss Ratio Method:
Estimating the aggregate loss charge

Answer 5

Question 6

Loss Ratio Method:
Advantages and Disadvantages

Answer 6

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 the type of exposures written

Question 7

Implied Development Method

Answer 7

Question 8

Implied Development Method:
Indexed LDFs

Answer 8

• To calculate limited LDFs for deductible loss, index limits for inflation:
  o This keeps the proportion of deductible/excess losses constant
  around the limit from year to year
  o 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 9

Implied Development:
Advantages and Disadvantages

Answer 9

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 10

Direct Development Method

Answer 10

Question 11

Credibility-Weighted Method formulas

Answer 11

Question 12

Credibility-Weighted Method:
Advantages and Disadvantages

Answer 12

Advantages
* Ties with pricing estimates for immature years where excess losses
haven’t emerged
* 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 13

Limited Severity Relativity

Answer 13

Question 14

Relationship between limited LDF,
unlimited LDF and severity relativities

Answer 14

Question 15

Relationship between XSLDF,
unlimited LDF and severity relativities

Answer 15

Question 16

Relationship between limited,
excess, and unlimited LDFs

Answer 16

Question 17

Relationship between limited severity relativities over time

Answer 17

Question 18

Distributional Model

Answer 18

Fit a model (e.g. Weibull) to severities in order to calculate consistent
severity relativities and LDFs.
→ This makes it easy to interpolate among limits and years
Distribution parameters vary over time by development period.
→ Parameters can be estimated by minimizing χ 2 between actual &
fitted severity relativities at the deductible size
→ Constrain parameters so that the model produces the actual unlimited
severity at maturity

Question 19

Partitioning expected development around the deductible limit

Answer 19

Question 20

Relationship of excess and limited development over time

Answer 20

As development age increases, an increasing proportion of development is
excess the deductible limit.

Question 21

Aggregate Loss Limit

Answer 21

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

Question 22

Collective Risk Model approach to Aggregate Limits

Answer 22

1) Model frequency and severity separately
→ Siewert uses Weibull for severity and Poisson for claim counts
2) Combine frequency and severity into a collective risk model
3) Sample from collective model to calculate development factors
→ Might improve by including parameter risk in the model
4) Use the BF method with LDFs from model to estimate losses excess
the aggregate limit

Question 23

Relationships regarding development of losses
excess of aggregate limits

Answer 23

• Development for losses excess aggregate limits decreases more rapidly
  over time with smaller deductibles than larger ones
  → Because most later development is in layers of loss above the
  deductible limit and not subject to the aggregate limit
• Development is more leveraged for larger aggregate limits
  → Takes longer for losses to breach the aggregate limit

Question 24

BF Method for Aggregate Limits

Answer 24

Question 25

Service Revenue

Answer 25

Revenue for an insurer to service claims under a high deductible program

Question 26

Service Revenue Asset Formulas

Answer 26

Question 27

Ways to handle allocated claims expense for high deductible programs

Answer 27

• Account manages the expense
  → Development patterns used should be loss-only
• Treated as loss and subject to limits
  → Should use loss + ALAE for development patterns