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

Theoretical Bayesian

  • Poisson - Binomial (1.2)

    • Use bayesian credibility: 1.8
  • Negative Binomial - Binomial (1.3)

    • Use bayesian credibility: 1.9

Bayesian Credibility

  • 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

    1. 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
    2. Use \(VHM\) and \(EVPV\) for \(Z\) if historical not a good predictor

  • Case load effect