27.4 Measuring the Variability of Chain Ladder Reserve Estimate - T. Mack

\(\star\) 3 different weight and variance assumptions from table 4.1

\(\star\) Mean squared error calculation

• The big MSE formula (4.4)

• How to get the \(\alpha\)’s we need for the MSE formula (4.5) and (4.6)

Confidence Interval

• Normal: equation (4.7)

• \(\star\) Log-normal: equation (4.8)

  • Use log-normal when \(s.e.(\hat{R}_i) > \dfrac{R_i}{2}\)

\(\star\) 4 test of assumptions to check

• Test 2. Residuals

  • Formula for residual (4.10)

• \(\star \star\) Test 3. CY Test

  • How to get \(z\) (4.11)

  • Expected value (4.12) and variance (4.13)

    • Or just memorize them up to 6 (Table 4.2)

• \(\star \star\) Test 4. Adjacent LDF Correlation

  • \(T\) for age \(k\) (4.15) and \(S\) (4.14)

  • \(T\) for the whole triangle (4.16)

  • CI to compare with resutls (4.17)

    • This is test at a lower CI