Chapter 1 Loss Development Using Credibility - E. Brosius
Least Square
Least Square formula (prop. 1.1) and Table 1.1
Know how to do them on the calculator (Notation for \(a\) and \(b\) on TI-30XS is flipped)
Remember to adjust for exposure if needed
Know the conclusions on LS
Know the caveat on least square
Additional considerations for calculations when using LS
Method comparisons
LS formula for each method (Table 1.1)
Pros and cons of each method
Theoretical Bayesian
Poisson - Binomial (1.2)
- Use bayesian credibility: 1.8
Negative Binomial - Binomial (1.3)
- Use bayesian credibility: 1.9
Best linear estimator formula (1.4)
- Know which method is best given the Cov and Var relationships (Table 1.2)
Development Formula: Use the credibility formula
Estimate from data (prop. 1.5): Same as the LS equation
- Alt form for \(Z\) with equation (1.1) that gives you same as LS results
Use \(VHM\) and \(EVPV\) for \(Z\) if historical not a good predictor