- TIA EXAM 5 - WERNER CH 12

• 1. Z must be greater than or equal to 0 and less than or equal to 1: No negative credibility and capped at fully credible
• 2. Z should increase as the number of risks underlying the actuarial estimate increases (all else equal)
• 3. Z should increase at a non-increasing rate

• Classical Credibility Approach
• Buhlmann Credibility
• Bayesian Analysis

• Most commonly used and therefore generally accepted
• Data required is readily available
• Computations are straightforward

Disadvantage: Simplifying assumptions may not be true in practice

• Exposures are homogeneous (i.e., same expected number of claims)
• Claim occurrence is assumed to follow a Poisson distribution
• No variation in the size of loss

To minimize the square error between estimate and true expected value

• Z = N / (N + K)
• K = EVPV / VHM

• Complement of credibility is given to the prior mean
• Risk parameters and risk process do not shift over time
• Expected value of the process variance of the sum of N observations increases with N
• Variance of the hypothetical means of the sum of N observations increases with N

• Advantage:
• Used within insurance industry & generally accepted

• Disadvantages:
• Difficult to get EVPV and VHM
• Simplyfying assumptions may not be true in practice

Based on fundamental notion that the prior estimate is adjusted to reflect the new information

More complex, less used

• 1. Accurate
• 2. Unbiased
• 3. Statistically Independent from Base Statistic
• 4. Available
• 5. Easy to Compute
• 6. Logical Relationship to Base Statistic

• 1. Available
• If not, then it is impractice to use

• 2. Easy to compute
• Especially important that calculations are easy to understand when need to file for state approval

• 3. Logical Relationship to Base Statistic
• Easier to justify to any 3rd party

• 1. Loss Costs of a Larger Group that Include the Group being Rated
• 2. Loss Costs of a Larger Related Group
• 3. Rate Change for the Larger Group Applied to Present Rates
• 4. Harwayne's Method
• 5. Trended Present Rates
• 6. Competitors' Rates

Because data split into classes, believe that experience is different, so combining classes introduces bias and the true expected losses will differ

• Advantage:
• Available,
• Easy to compute, and
• some logical connection

• Disadvantage:
• Not independent because subject experience is included in group experience. (Not big issue if subject experience doesn't dominate the group)

Biased & True expected loss experience will differ b/c recombining classes makes hetero grps

• Similar to large group including class in that it is biased and true expected losses differ: May make adjustment for bias to related experience to match exposure to loss
• Advantage:
• Is independent - which may make it a better choice than large group including class

• Available,
• easy to compute, and
• some logical connection if groups closely related:

Note - if adjustment made for bias, may be more difficult to compute

Disadvantage:

• Biased &
• True expected loss experience will differ b/c recombining classes makes hetero grps

• Current Loss Cost of Subject Experience (CLCSE)
• C = CLSCE x (LargerGrpIndLC / LargerGrpCurrLC)

• Advantage:
• Largely unbiased and
• likely accurate over the long term assuming rate changes are small

• Typically is available,
• easy to compute, and
• logical that rate change of bigger group is indicative of rate change of subject experience

Independence depends on size of subject experience relative to the larger group

• *Compute the state overall means with the base state class distribution
• *Compute individual state adjustment factors by dividing subject average PP by adjusted related state PP
• *Multiply each related state's base class by state adjustment factor to get adjusted state class rates
• *Complement equals the exposure weighted average of the adjusted related state rates

• Advatages:
• Unbiased as it adjusts for distributional differences
• Use of multi-state data generally implies it is reasonably accurate: Need enough data to minimize process variance
• Mostly independent since subject and related experience from different states
• DIS:
• Data is available, but computations can be time consuming
• Logical relationship, but may be harder to explain due to calculation complexity

• Current rates should be adjusted for the previously indicated rate, not what was implemented
• Trend period (t) taken from original target eff date of current rates to planned eff date
• Changes in loss cost levels:
• May be due to:
• inflation,
• distributional shifts,
• safety advances, etc.;

• Present Rate (PR)
• Loss Cost Implemented with Last Review (LCILR)
• t= trend period
• C = PR x (Trend ^ t) x (Prev Ind LC/LCILR) - 1

C = (LossTrndFact/PremTrndFact) x (1 + prior ind / 1 + prior rate chg)

• Advantages:
• Unbiased
• Available
• Easy to compute
• Easy to explain

• Disadvantage
• Accuracy depends on process variance of historical loss
• Independence depends on experience used

• Must consider marketing practices and judgment of the competitor and effects of regulation: Can cause inaccuracy
• Competitors may have different underwriting and claims practices that creates bias
• Advantage
• Independent
• Generally accepted by regulators because of logical relationship: May be the only choice
• Disadvantage:
• Not Available: Calculations may be straightforward but getting the data may be difficult

• 1. Issues:
• Excess ratemaking deals with volatile lines and low volumes of data
• Due to low volume, often use loss costs below attachment point to predict excess losses
• Slow development and trend in excess layers can also complicate projections
• 2. Increased Limits Factors (ILF)
• 3. Lower Limits Analysis
• 4. Limits Analysis
• 5. Fitted Curves

• PA x {(ILF @ A + L) / (ILF @ A )- 1}
• If subject experience has different size of loss distribution than used in developing the ILFs, procedure will be biased and inaccurate, but often best available estimate
• Error associated with estimate tends to be independent of error associated with base statistic
• Data needed incl ILFs and ground-up losses that haven't been truncated below attachment
• Ease of computation - Easiest of the excess complements to compute
• Explainable relationship - Controversial; more logically related to losses below attach point
• Advantage:
• Independent
• Easy to Compute
• Explainable relationship
• Disadvantage:
• Biased
• Inaccurate

• Pd x (ILF @ A + L - ILF @ A) / ILF @ d
• Disadvantage
• Bias - losses far below attachment point accentuates the impact of variations in loss severity distributions
• Advantages:
• Losses capped at lower limit may increase stability and accuracy
• Error associated with estimate tends to be independent of error associated with base statistic
• Data a little more available since losses capped at lower limit
• Ease of computation - Just slightly more complex than 1st method
• Explainable relationship - Controversial for same reason as first method

• LR x Sum(Pd x (ILF @ min(d, A+L) - ILF @ A) / ILF @ d)
• Analyze each limit of coverage separately
• Assume all limits will experience same loss ratio
• Calculate total loss cost (Prem x ELR) for each layer
• Use ILFs to calculate % loss in layer
• Multiply loss cost from layer by calculated %

• Biased and inaccurate to same extent as prior two methods, plus assumes LR doesn't vary by limit
• Typically used by reinsurers that don't have access to the full loss distribution
• Calculations are straightforward but take more time than the first two methods
• Explainable relationship - Controversial for same reason as other methods

• Tends to be less biased and more stable, assuming curve replicates general shape of actual data, and signicantly more accurate when few claims in excess layer
• Less independent due to reliance on larger claims to fit curve
• Most complex procedure and requires data that may not be readily available
• Most logically related to losses in layer, but complexity may make it hard to communicate

• Statistical diagnostics provided with the model results used to see how meaningful results are
• Modeler considers this when selelcting final model & rates
• Informs of overall appropriateness of model assumptions
• Typical results of multivariate classification analysis are NOT credibility-wtd with trad actuarial estimates