General approaches to evaluate excess ult. loss
Loss Ratio Approach
Implied Development Approach
Direct Development Approach
BF approach
Loss Ratio Approach when to use
When no data is available
Use for immature years where data is sparse
Loss Ratio Approach steps
get per occ excess losses
get per agg excess losses
add together above two
Pros and Cons for Loss Ratio Approach
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
Implied development approach steps
- 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
Benefits of high deductible programs
- 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
How to estimate the overall reserve while reflecting differing mixes of deductibles and limits
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
Selecting the Loss Ratio for the Loss Ratio Method
- 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
Loss Ratio Method:
Estimate of per-occurrence excess losses
Loss Ratio Method:
Estimating the aggregate loss charge
Loss Ratio Method:
Advantages and Disasvantages
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
Implied Development Method
- 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
Implied Development Method:
Indexed LDFs
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
Implied Development: Advantages and Disadvantages
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
Direct Development Method
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
Credibility-Weighted Method formula
Credibility weighted method: Advantages and Disadvantages
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
Limited Severity Relativity
Ratio between limited and unlimited severity
Relationship between limited LDF, unlimited LDF, and severity relativities
C = counts
S = severity
R = severity relativity
t = age
L = limit
Relationship between XSLDF, unlimited LDF, and severity relativities
Relationship between Limited, XS, and unlimited LDFs
Relationships between limited severity relativities over time
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
Distributional Model
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
Partitioning expected development around the deductible limit
