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Loss Reserve Variability Using DFA Approaches

Loss Reserve Variability Using DFA Approaches. Casualty Loss Reserve Seminar September 19, 2000 Minneapolis. Loss Reserves in DFA. Speakers Chuck Emma, Paratus Consulting Limited Basic reserve modeling for unanticipated inflation Susan Witcraft, Milliman & Robertson

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Loss Reserve Variability Using DFA Approaches

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  1. Loss Reserve VariabilityUsing DFA Approaches Casualty Loss Reserve Seminar September 19, 2000 Minneapolis

  2. Loss Reserves in DFA Speakers • Chuck Emma, Paratus Consulting Limited Basic reserve modeling for unanticipated inflation • Susan Witcraft, Milliman & Robertson Modeling non-inflation variability • Nylesh Shah, PriceWaterhouse Coopers, LLP Reserve risk factor analysis

  3. Basic Reserve ModelingOverview General Concepts Basic Illustration of Reserve Variability • Randomness in future loss payouts • Unanticipated inflation

  4. Basic Reserve ModelingGeneral Concepts Which reserve elements to model? • payment dollars • payout percentages Which risk factors to model? • economic inflation • social inflation • extra-normal shifts Best Estimates vs. Recorded Reserves

  5. Basic Reserve ModelingGeneral Concepts (cont’d) Which results to measure? Validation Metrics • Dependency (correlation) with inflation • Autocorrelation across accident years • Autocorrelation across payment lags Performance Metrics • Schedule P development • Future calendar year impact • Future surplus position

  6. Basic Reserve ModelingIllustration Notion Future loss payments (reserves) vary, relative to a-priori expectations, due to two drivers: • Unexpected inflation • Pure randomness Loss Reserve Development = (A-Priori Loss Payments) – (Generated Loss Payments)

  7. Basic Reserve ModelingIllustration (cont’d) Single Accident Year (2000) - Example

  8. Basic Reserve ModelingIllustration (cont’d) Overall Modeling Process Step 1: Parameterize (by Line) A. Estimate mean and variability of loss payout patterns percentages (piecewise) B. Define expected loss reserve inflation factor (adequacy parameter), say 6.0%.

  9. Basic Reserve ModelingIllustration (cont’d) Step 1 (cont’d) Expected Reserve Payout Pattern

  10. Basic Reserve ModelingIllustration (cont’d) Step 1 (cont’d) Resultant A-Priori (Static) Reserve Schedule

  11. Basic Reserve ModelingIllustration (cont’d) Step 2: Generate Stochastic Inflation Path

  12. Basic Reserve ModelingIllustration (cont’d) Step 3: Generate Payout Percentages A-Priori Generated

  13. Basic Reserve ModelingIllustration (cont’d) Step 3 (cont’d) Generated Reserve Payout Pattern

  14. Basic Reserve ModelingIllustration (cont’d) Step 4: Combine the two to calculate future loss payments (for accident years 1995-1999)

  15. Basic Reserve ModelingOther Thoughts What if Costs Shift Suddenly? • Mass tort emergence • Expanded liability • Tort reform Some Ideas • Stochastic shocks to inflation modeling • Varying payouts over relevant accident year • Individual policy modeling (limit stacking)

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