[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **Ultimate Loss** ## Definition ==Ultimate Loss== Ultimate loss is the total projected cost of all claims for a given exposure period, including both payments already made and reserves for future payments. ## Formula ``` Ultimate Loss = Paid Losses + Case Reserves + IBNR Or equivalently: Ultimate Loss = Reported Losses + IBNR Where: Reported = Paid + Case Reserves ``` ## Estimation Methods ### Chain Ladder ``` Ultimate = Reported × CDF ``` ### Bornhuetter-Ferguson ``` Ultimate = Reported + (Expected × % Unreported) ``` ### Expected Loss ``` Ultimate = Expected Loss Ratio × Earned Premium ``` ## Uses ### Reserving - Determine reserve adequacy - Calculate IBNR - Financial statement preparation ### Ratemaking ``` Loss Ratio = Ultimate Losses / Earned Premium Used for rate indications ``` ### Pricing - Estimate expected costs - Set premiums - Risk assessment ## Example Projection ``` AY 2023 @ 12 months: Paid: $300,000 Case Reserves: $200,000 Reported: $500,000 Method 1 - Chain Ladder: 12-Ult CDF: 2.400 Ultimate = $500,000 × 2.400 = $1,200,000 Method 2 - BF: Expected: $1,000,000 % Unreported: 58.3% Ultimate = $500,000 + ($1,000,000 × 0.583) = $1,083,000 Selected Ultimate: $1,140,000 (blend) ``` ## Related Concepts - [[IBNR Reserves]] - [[Case Reserves]] - [[Development Factor]] - [[Chain Ladder Method]] ## References - Friedland, Chapters 1-5