Chapter 4 Measuring the Variability of Chain Ladder Reserve Estimate - T. Mack

\(\star\) 3 underlying assumptions of chain ladder that makes the implicit assumptions hold and when they might be violated

1. Expected incremental losses are \(\propto\) losses to date, dependent on age (prop. 4.1)

2. Losses in each AY are \(\perp\!\!\!\!\perp\) of the losses in other AYs (prop. 4.2)

3. Variance of the incremental losses is \(\propto\) losses reported to date dependent on age (prop. 4.3)

\(\star\) 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 \(s.e.(\hat{R}_i) > \dfrac{R_i}{2}\)

\(\star\) When the above assumptions might be violated and know the 4 test of assumptions to check

• Test 1. Intercept

• Test 2. Residuals

  • Formula for residual (4.10)

• 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)

• 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

  • This is similar to Venter’s test

  • Why test the whole triangle versus just pairs of LDFs