Mack

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 B-F and C-L Methods
- 1. Generally has a lower mean squared error
- 2. Found to be almost as precise as an exact Bayesian procedure
- 3. Outperforms the B-F and C-L methods in many situations
Mack's Formula for Reserve Estimate Using Gunnar Benktander Method (RGB)
- RGB = q_kU_BF or p_kR_CL + (1 - p_k)R_BF where
- 1. U_BF = Estimate of ultimate losses using B-F method
- 2. RCL = Reserve estimate using Chain Ladder method
- 3. R_BF = Reserve estimate using B-F 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_k²)U_CL + q_k²U₀ where
- 1. U_CL = Estimate of ultimate losses using LDF method
- 2. U₀ = 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

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Esaie

26176

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Mack

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Updated

2010-07-09T20:13:27Z

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