[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **Large Loss** ## Definition ==Large Loss== is a claim of unusual size that exceeds typical loss amounts for a line of business, requiring special treatment in ratemaking and reserving to avoid distortion. ## Characteristics - Significantly exceeds normal claim size - Low frequency, high severity - Can distort historical patterns - May be unique or non-recurring - Affects rate indications materially ## Identification Criteria ### Statistical Threshold ``` Common definitions: - Exceeds X percentile (e.g., 95th) - Exceeds X standard deviations from mean - Exceeds $X threshold (e.g., $100,000) - Exceeds X% of premium ``` ### Judgment Factors - Unusual circumstances - Non-recurring nature - Policy limits consideration - Line of business norms ## Treatment in Ratemaking ### Capping ``` Limit large losses to threshold: Example: Actual loss: $500,000 Cap at: $250,000 Use $250,000 in rate indication Reduces volatility but may understate costs ``` ### Exclusion ``` Remove large losses entirely: Restate experience excluding shock losses Adjust exposure to reflect capped coverage May add separate load for large loss potential ``` ### Separate Treatment ``` Analyze large losses separately: - Historical frequency of large losses - Average size when they occur - Separate provision in rates ``` ### Full Inclusion ``` Include all losses as reported: - No special treatment - Appropriate if predictable - Requires sufficient volume ``` ## Example ``` Workers Compensation Rate Indication: Experience includes: - 995 normal claims averaging $10,000 - 5 large claims totaling $1,000,000 Options: 1. Full inclusion: All losses = $11,000,000 2. Cap at $100,000: $10,450,000 + allowance 3. Exclude & load: $9,950,000 + 10% load 4. Separate analysis: Normal + Large loss provision ``` ## Reserving Considerations - Large losses may develop differently - Case reserves may be less adequate - Higher uncertainty in ultimate cost - May need special review ## Related Concepts - [[Catastrophe Loss#Definition]] - [[Extraordinary Loss#Definition]] - [[Large Loss Capping#Definition]] - [[Large Loss Exclusion#Definition]] ## References - Werner & Modlin, Chapter 9