Chapter 3 Credible Claims Reserve: Benktander, Neuhaus and Mack - W. Hurlimann

Everything is based on a special method to calculate the \(ELR\) and \(LDFs\)

• \(ELR\) is based on the whole triangle \(\sum\)-ing up column incremental LRs

• \(LDFs\) are based \(\dfrac{\text{Col LRs}}{ELR}\)

• Key is just to watch out for the given data is incremental vs cumulative

Know the \(Z\) for different methods (Table 3.1)

• The \(Z\) is for weighting the reserve

• Optimal credibility formula assumes:

  • \(U_i^{BC} {\perp\!\!\!\!\perp} \: C_i\) and \(R_i\)

  • \(\mathrm{Var}(U_i) = \mathrm{Var}(U_i^{BC})\)

• Basis of optimal credibility 3.2

• MSE for the credibility formula

All the methods can be done using traditional LDFs

• Remember “shortcuts” to calculate the CDFs given incremental triangles

• Also shortcut to calculate the unpaid based on total “unused” premium