# A.4. Mahler 1 - Credibility

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1. Advantages of using baseball data
• constant set of risk, vs insurance where risks leave or enter the database
• loss data is readily available, accurate and final
• each team plays roughly the same number of games (i.e. no consideration for size of risk)
2. Testing for differences between teams
• calculate average and standard deviation of losing % by team
• compare to binomial distribution with p = 50%, σ = √[np(1 - p)]
• since many teams losing percentage is outside of , conclude teams are different
3. Testing for shifting risk parameters - standard 𝝌2 test
• test if the risk process could have the same mean over period
• compare 5 years actual losses vs expected losses
• 𝝌2 test = ∑(Actual - Expected)2/Expected
• 𝝌2 has n - 1 d.f. → compare to tabular value (higher = confirms risks are different)
4. Testing for shifting risk parameters - correlations test
• compute correlation between the results for all risks for pairs of years
• take average correlation with a given difference in time
• examine how the average correlation depends of this time difference
• correlation decreases over time, which wouldn't be the case if parameters were stable
• however it's high for small time difference, suggesting there’s value to using recent experience to predict the future.
5. Credibility weighting methods
• every risk is average: only use μ = 50%
• most recent years repeat: use 100% credibility on the latest year
• most recent year and μ: Z * most recent year, (1 - Z) * μ
• equal weight to most recent years: Z/N for the N most recent years, Z to μ
• exponential smoothing: apply Z to prior year actual, and (1 - Z) to prior year estimate
• generalized method: apply given factors Zi to prior years, and what’s left to μ
6. Criteria to decide between solutions
• least square error: smaller the MSE, the better the solution
• limited fluctionation: Pr(act > k% different from est) = Pr(|Xest - Xact|/Xest> k%) < P
• Meyers/Dorweiler: calculate correlation between actual/predicted, and predicted/overall actual mean; want correlation as close to zero as possible using Kendall 𝝉; this would confirm that there is no evidence that large predictions lead to large errors and small predictions lead to small errors
7. Meyers/Dorweiler vs Other Criteria
• least square & limited fluctuations both attempt to eliminate large errors
• Meyers/Dorweiler is concerned with the pattern of the errors. Large errors are not a problem, as long as there is no pattern relating errors to experience rating modifications
• Most actuaries would lean towards least square & limited fluctuations
8. Conclusion
• when there are shifting risk parameters, older years are less relevant in predicting the future
• not having the most recent year of historical data significantly increase the SSE of estimate

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 Author: EExam8 ID: 305185 Filename: A.4. Mahler 1 - Credibility Updated: 2015-09-05 13:07:47 Tags: Mahler Credibility Folders: Description: Mahler 1 - Credibility and Shifting Risk Parameter Show Answers:

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