Mack
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Mack's Formula for Ultimate Losses
 U = C_{k} + R, where
 1. U = Ultimate Claims
 2. C_{k} = Claims amount paid up to time k
 3. R = Reserve Estimate

Advantages of Benktander Method over BF and CL Methods
 1. Generally has a lower mean squared error
 2. Found to be almost as precise as an exact Bayesian procedure
 3. Outperforms the BF and CL methods in many situations

Mack's Formula for Reserve Estimate Using Gunnar Benktander Method (RGB)
 RGB = q_{k}U_{BF} or p_{k}R_{CL} + (1  p_{k})R_{BF} where
 1. U_{BF} = Estimate of ultimate losses using BF method
 2. RCL = Reserve estimate using Chain Ladder method
 3. R_{BF} = Reserve estimate using BF method
 4. p_{k} = proportion of ultimate claims amount paid at time k = 1=ULD_{k}
 5. q_{k} = proportion of ultimate claims amount unpaid at timek = 1  p_{k}

Mack's Formula for Ultimate Losses Using Gunnar Benktander Method (UGB)
 U_{GB} = C_{k} + R_{GB} = (1  q_{k}^{2})U_{CL} + q_{k}^{2}U_{0} where
 1. U_{CL} = Estimate of ultimate losses using LDF method
 2. U_{0} = Estimate of ultimate losses prior to taking claims experience into account
 3. R_{GB} = Reserve estimate using Gunnar Benktander method
 4. C_{k} = Claims paid to date at period k
 5. q_{k} = proportion of ultimate claims amount unpaid at timek = 1  pk