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Mack Benktander

Synopsis

Be able to calculate Ultimate losses, using expected claims, BF and Benktander iterations, and be clear about the strengths of each method.

Study Strategy

  • I solved around 70% of the questions which are almost the same type. Just know the formulae intuitively and what \(U^{(0)}, U^{(1)}, U^{(2)}\) represent.

My Notes

  • Why Benktander is better than BF?
    1. BF doesn't use actual losses to estimate RESERVES, where as Benktander does use it.
  • Benktander better than CL?
    1. Benktander gives some weight to a priori estimate, which helps temper the volatility of estimates especially in immature years.
  • In general,
    • Benktander method has lower MSE than the BF method. (Walter Neuhaus compared with \(c^*\)1, this happens when \(c^*\) is closer to \(p_{k}\) than 0, i.e. \(c^* \gt p_{k}/2\)). Mack states that this happens almost all the time (Benktander MSE is lower than that of BF and CL)
  • Problem with BF: Reserves rely entirely on the a priori loss estimate, thus it isn't as responsive to actual losses as the chain ladder method.
  • Can you verbally describe the Benktander method?
    1. It is the credibility weighting of the Chain Ladder and BF methods,
    2. giving weight Z = % reported to the chain ladder method,
    3. and (1-Z) to the BF method.
\[ U^{(n)} = (1- q_{k}^n)U_{CL} + q_{k}^nU_{0} \]

and note that \(U^{(0)} = U_{0}\), \(U^{(1)} = U_{BF}\) and \(U^{(2)} = U_{GB}\).

  1. Optimal credibility reserve that minimizes the MSE ↩