1. Necessary Criteria for Measures of Credibility
    • 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
  2. Methods for Determining Credibillity of an Estimate
    • Classical Credibility Approach
    • Buhlmann Credibility
    • Bayesian Analysis
  3. Advantages & Disadvantage of the classical credibility approach
    • Most commonly used and therefore generally accepted
    • Data required is readily available
    • Computations are straightforward

    Disadvantage: Simplifying assumptions may not be true in practice
  4. Simplifying assumptions about observed experience using Classical Credibility Approach
    • 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
  5. What is the Goal of Buhlmann Credibility?
    To minimize the square error between estimate and true expected value
  6. Formula for credibility using Buhlmann Credibility
    • Z = N / (N + K)
    • K = EVPV / VHM
  7. Assumptions using Buhlmann Credibility
    • 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
  8. Advantage & Disadvantages of Buhlmann Credibility
    • Advantage:
    • Used within insurance industry & generally accepted

    • Disadvantages:
    • Difficult to get EVPV and VHM
    • Simplyfying assumptions may not be true in practice
  9. Describe the Bayesian Analysis
    Based on fundamental notion that the prior estimate is adjusted to reflect the new information

    More complex, less used
  10. Desirable Qualities of a complement of Credibility
    • 1. Accurate
    • 2. Unbiased
    • 3. Statistically Independent from Base Statistic
    • 4. Available
    • 5. Easy to Compute
    • 6. Logical Relationship to Base Statistic
  11. Describe three of the Desirable qualities of credibility
    • 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
  12. Complement of Credibility for First Dollar Ratemaking
    • 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
  13. Evaluation of Loss Costs of a Larger Group that Include the Group being Rated
    Because data split into classes, believe that experience is diff erent, so combining classes introduces bias and the true expected losses will diff er

    • 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
  14. Evaluation of Loss Costs of a Larger Related Group
    • Similar to large group including class in that it is biased and true expected losses diff er: 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


    • Biased &
    • True expected loss experience will differ b/c recombining classes makes hetero grps
  15. Evaluation of Rate Change for the Larger Group Applied to Present Rates
    • 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
  16. Calculations in Harwayne's Method
    • *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
  17. Evaluation of Harwayne's Method
    • Advatages:
    • Unbiased as it adjusts for distributional diff erences
    • 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 diff erent states
    • DIS:
    • Data is available, but computations can be time consuming
    • Logical relationship, but may be harder to explain due to calculation complexity
  18. Trended Present Rates
    • 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.;
  19. Complement for the Pure Premium Approach
    • Present Rate (PR)
    • Loss Cost Implemented with Last Review (LCILR)
    • t= trend period
    • C = PR x (Trend ^ t) x (Prev Ind LC/LCILR) - 1
  20. Complement for an indicated rate change when using the Loss Ratio Approach
    C = (LossTrndFact/PremTrndFact) x (1 + prior ind / 1 + prior rate chg)
  21. Evaluation of Trended Rates
    • Advantages:
    • Unbiased
    • Available
    • Easy to compute
    • Easy to explain

    • Disadvantage
    • Accuracy depends on process variance of historical loss
    • Independence depends on experience used
  22. Evaluation of Competitors' Rates
    • Must consider marketing practices and judgment of the competitor and effects of regulation: Can cause inaccuracy
    • Competitors may have di fferent 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
  23. Excess Ratemaking - products that cover claims that exceed some attachment point
    • 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
  24. Evaluation of Increased Limits Factors (ILF)
    • PA x {(ILF @ A + L) / (ILF @ A )- 1}
    • If subject experience has diff erent 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
  25. Evaluation of Lower Limits Analysis
    • 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
  26. Calculation of Limits Analysis
    • 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 %
  27. Evalution of Limits Analysis
    • 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
  28. Evaluation of Fitted Curves
    • 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
  29. Describe what happens when credibility is used with statistical methods
    • 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
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