Werner Ch 12

  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 of the classical credibility approach
    • Most commonly used and therefore generally accepted
    • Data required is readily available
    • Computations are straightforward
  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. Formula for credibility using Buhlmann Credibility
    • Z = N / (N + K)
    • K = EVPV / VHM
  6. 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
  7. 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
  8. 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
  9. 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
    • Not independent because subject experience is included in group experience. However, may not be big issue if subject experience doesn't dominate the group
    • Typically is available, easy to compute, and some logical connection
  10. 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
    • Is independent - which may make it a better choice than large group including class
    • Typically is available, easy to compute, and some logical connection if groups closely related: Note - if adjustment made for bias, may be more difficult to compute
  11. Evaluation of Rate Change for the Larger Group Applied to Present Rates
    • Current Loss Cost of Subject Experience (CLCSE)
    • C = CLSCE x (LargerGrpIndLC / LargerGrpCurrLC)
    • Largely unbiased and likely accurate over the long term assuming rate changes are small
    • Independence depends on size of subject experience relative to the larger group
    • Typically is available, easy to compute, and logical that rate change of bigger group is indicative of rate change of subject experience
  12. 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
  13. Evaluation of Harwayne's Method
    • 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
    • Data is available, but computations can be time consuming
    • Logical relationship, but may be harder to explain due to calculation complexity
  14. Trended Present Rates
    • Current rates should be adjusted for the previously indicated rate, not what was implemented
    • Changes in loss cost levels: May be due to inflation, distributional shifts, safety advances, etc.; Trend period (t) taken from original target eff date of current rates to planned eff date
  15. Complement for the Pure Premium Approach
    • Present Rate (PR)
    • Loss Cost Implemented with Last Review (LCILR)
    • C = PR x Trend ^ t x (PrevIndLC/LCILR) - 1
  16. Complement for an indicated rate change when using the Loss Ratio Approach
    C = (LossTrndFact/PremTrndFact) x (1 + prior ind / 1 + prior rate chg)
  17. Evaluation of Trended Present Rates
    • Accuracy depends largely on process variance of historical loss costs: Primarily used for indications with large amounts of data
    • Unbiased since pure trended loss costs are unbiased
    • Independence depends on experience used: If complement comes from a review that used data from 2007 - 2009 and subject experience is from 2008 - 2010, then they are not independent
    • Data is readily available, easy to compute, and is easily explainable
  18. 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
    • Will be independent
    • Calculations may be straightforward but getting the data may be difficult
    • Generally accepted by regulators because of logical relationship: May be the only choice
  19. 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
  20. 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
  21. Evaluation of Lower Limits Analysis
    • Pd x (ILF @ A + L - ILF @ A) / ILF @ d
    • Even more prone to bias than fi rst method because losses far below attachment point accentuates the impact of variations in loss severity distributions
    • 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
  22. 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 %
  23. 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
  24. 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
Card Set
Werner Ch 12
Exam 5 TIA Werner ch 12