Werner Ch 12

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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
• Buhlmann 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 Buhlmann Credibility
• Z = N / (N + K)
• K = EVPV / VHM
6. Assumptions using Buhlmann 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
 Author: Esaie ID: 15379 Card Set: Werner Ch 12 Updated: 2010-04-20 19:17:40 Tags: Exam TIA Werner Folders: Description: Exam 5 TIA Werner ch 12 Show Answers: