A.4. Mahler 1 - Credibility

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A.4. Mahler 1 - Credibility
2015-09-05 09:07:47
Mahler Credibility

Mahler 1 - Credibility and Shifting Risk Parameter
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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