Cas Exam 8 Mahler 1

Front 1

Simplifications in baseball data compared to insurance data

Back 1

1. A constant set of risks (teams).
2. The baseball loss data is readily available, accurate, and not subject to development.
3. Each risk (team) is of equal size; they each play roughly the same # of games each year.

Front 2

Tests to determine if risk parameters are shifting over time.

Back 2

1. Chi-squared test. For each risk, calculate Chi-squared as sum((actual_i-Expected_i)^2/(Expected_i). If there are n time period groups, the chi-square table value to compare against will have n-1 degrees of freedom. If the test statistic exceeds the tabular value with the acceptable percentage level, then conclude that the distributions are different, and thus risk parameters for that risk have shifted over time.
2. Compare correlations between years (1-year intervals, 2-year intervals, etc. If correlation decreases with time, shifting parameters over time.)

Front 3

6 methods to estimate X

Back 3

1. X = mu population mean
2. X = Y1 Most recent year (100% cred)
3. X = Z*Y1 + (1-Z)*mu
4. X = Z/n*sum(Y_i) + (1-Z)*mu
5. Xest,i+1 = Z*Y_i + (1-Z)*Xest,i
6. X = sum(Z_i*Y_i) + (1-sum(Z_i))*mu

Front 4

3 criteria to evaluate possible estimates

Back 4

1. Least squared error - calculate the mean squared error of the prediction compared with the actual observed result. The Buhlmann/Bayesian credibility methods attempt to minimize this criteria.
2. Limited Fluctuation - Also known as Small Chance of Large Errors. Measure the probability that the observed result differs more than a certain percent from the predicted result. The classical credibility method targets this criteria.
3. Meyers/Dorweiler - Calculate the correlation between the ratio of actual to expected losses and the ratio of predicted losses to overall losses. This criteria confirms that there is no evidence that large predictions lead to large errors and small predictions lead to small errors.