[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **IBNR Reserves** ## Definition ==IBNR Reserves== IBNR (Incurred But Not Reported) reserves represent estimated losses for claims that have occurred but have not yet been reported to the insurance company, plus development on reported claims. ## Components ### Pure IBNR Claims that have occurred but not yet reported: - Accident happened - Insured unaware or hasn't reported - Insurer has no knowledge ### Development on Reported Claims Increase in known claims beyond case reserves: - Case reserves inadequate - Future developments unknown - Additional payments expected ### Total IBNR Formula ``` Total IBNR = Ultimate Losses - Reported Losses Where: Reported Losses = Paid + Case Reserves ``` ## Calculation Methods ### Chain Ladder ``` Ultimate = Reported × CDF IBNR = Ultimate - Reported ``` ### Bornhuetter-Ferguson ``` IBNR = Expected Losses × % Unreported Ultimate = Reported + IBNR ``` ### Expected Loss ``` Ultimate = Expected Loss Ratio × Earned Premium IBNR = Ultimate - Reported ``` ## Example ``` AY 2023 @ 12 months: Paid Losses: $300,000 Case Reserves: $200,000 Reported Losses: $500,000 Using Chain Ladder (CDF = 2.400): Ultimate = $500,000 × 2.400 = $1,200,000 Total IBNR = $1,200,000 - $500,000 = $700,000 Breakdown: Pure IBNR (unreported claims): ~$400,000 Development on reported: ~$300,000 Total IBNR: $700,000 ``` ## Factors Affecting IBNR ### Reporting Lag - Time from accident to report - Long-tail lines: Higher IBNR - Short-tail lines: Lower IBNR ### Line of Business Characteristics ``` Workers Comp: - Long tail - High IBNR ratio - Slow reporting Auto Physical Damage: - Short tail - Low IBNR ratio - Fast reporting ``` ### Claims Processing - Settlement practices - Case reserve adequacy - Claim department efficiency ## IBNR by Maturity ### Recent Accident Years - High IBNR percentage - Many unreported claims - Limited development ### Middle Years - Moderate IBNR - Mostly development on reported - Some pure IBNR remains ### Mature Years - Low IBNR percentage - Primarily development - Few unreported claims ## Example by Line ``` Workers Compensation: AY 2024 @ 12 months Reported: $500,000 (20% of ultimate) IBNR: $2,000,000 (80% of ultimate) Ultimate: $2,500,000 Auto Physical Damage: AY 2024 @ 12 months Reported: $900,000 (90% of ultimate) IBNR: $100,000 (10% of ultimate) Ultimate: $1,000,000 ``` ## Financial Statement Impact ### Balance Sheet ``` Loss Reserves = Case Reserves + IBNR Components: - Case reserves: Claim-specific estimates - IBNR: Actuarial estimate ``` ### Income Statement ``` Incurred Losses = Paid + Δ Reserves Reserve change includes: - Changes in case reserves - Changes in IBNR estimates ``` ## Related Concepts - [[Case Reserves]] - [[Ultimate Loss]] - [[Chain Ladder Method]] - [[Development Factor]] - [[Reported Losses]] ## References - Friedland, Chapter 1 - ASOP 43