3.2 Remark 6.1

Doing all the above with more “Traditional” method

• Chainladder

  • Replace \(p_k\) with \(p_k^{CL}\), inverse of the CDF

  • \(R^{ind}_i = \dfrac{C_i}{p_k} - C_i\)

• Cape Cod

  • \(ELR = \dfrac{\sum\limits_{i,k}S_{ik}}{\sum\limits_i V_i \times p_i^{CL}}\)

    Sum of cumulative paid loss \(\div\) used up premium

  • \(R^{Coll}_i = q_k \times (V_i \times ELR)\)

• Benktander with \(Z_i = p_k\)

  • \(R^{GB}_i = Z_i \times R^{ind}_i + (1 - Z_i) \times R^{coll}_i\)

• Optimal Cape Cod with \(Z_i = \dfrac{p_k}{p_k+\sqrt{p_k}}\)

• BF use some other a-priori that varies by AY and \(Z = 0\)

  • Note that we are talking about applying \(Z\) to the formula above (Not the weighting between ultimates)