[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **Benktander Method** ## Definition ==Benktander Method== The Benktander method is a reserving technique that iteratively combines the Chain Ladder and Bornhuetter-Ferguson methods, providing estimates that fall between these two approaches. ## Formula ``` One iteration: Ultimate = Reported + [(Expected - Reported) × % Unreported] Where: Expected = a priori expected ultimate or prior estimate % Unreported = 1 - (1/CDF) ``` ## Relationship to Other Methods ### After 0 iterations: Expected Loss Method ``` Ultimate = Expected Losses (Ignores reported entirely) ``` ### After 1 iteration: Bornhuetter-Ferguson ``` Ultimate = Reported + (Expected × % Unreported) ``` ### After ∞ iterations: Chain Ladder ``` Ultimate = Reported × CDF (Ignores expected entirely) ``` ### Standard Benktander: 2 iterations Provides middle ground between BF and CL ## Methodology ### Iteration 1 (BF Method) ``` Ultimate₁ = Reported + (Expected₀ × % Unreported) ``` ### Iteration 2 (Benktander) ``` Ultimate₂ = Reported + [(Ultimate₁ - Reported) × % Unreported] ``` ## Example ``` Given: Reported: $600 Expected: $1,000 CDF: 2.000 % Unreported: 50% Iteration 0 (Expected): Ultimate₀ = $1,000 Iteration 1 (BF): Ultimate₁ = $600 + ($1,000 × 0.50) = $600 + $500 = $1,100 Iteration 2 (Benktander): Ultimate₂ = $600 + [($1,100 - $600) × 0.50] = $600 + ($500 × 0.50) = $600 + $250 = $850 Chain Ladder: Ultimate_CL = $600 × 2.000 = $1,200 Summary: Expected: $1,000 BF: $1,100 Benktander: $850 Chain Ladder: $1,200 ``` ## Credibility Interpretation Benktander can be viewed as assigning different credibility: - More weight to actual emergence than BF - Less weight than Chain Ladder - Compromise between the two ## When to Use **Advantages:** - Moderates between BF and CL - More responsive than BF - More stable than CL - Good for middle-maturity years **Use when:** - Transitioning from BF (immature) to CL (mature) - Want compromise between methods - Actual emergence becoming credible - BF too stable, CL too volatile ## Related Concepts - [[Bornhuetter-Ferguson Method]] - [[Chain Ladder Method]] - [[Expected Loss Method]] ## References - Friedland, Chapter 5 - Benktander, "An Approach to Credibility in Calculating IBNR"