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Property-Liability Insurance Loss Reserve Ranges Based on Economic Value

Property-Liability Insurance Loss Reserve Ranges Based on Economic Value. Alfred Au and Liang Zhang. Overview. Background of research Methodologies Results Feedback. Background. Traditional loss reserving methods Nominal, undiscounted, for statutory requirements

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Property-Liability Insurance Loss Reserve Ranges Based on Economic Value

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  1. Property-Liability Insurance Loss Reserve Ranges Based on Economic Value Alfred Au and Liang Zhang

  2. Overview • Background of research • Methodologies • Results • Feedback

  3. Background • Traditional loss reserving methods • Nominal, undiscounted, for statutory requirements • Impacts of inflation on traditional methods

  4. Background • Recent Developments • ALM • FASB & IASC: “Fair Value” • CEA: Solvency II • S&P criticism

  5. Trends in Inflation

  6. Trends in Inflation • Increasing oil prices • Depreciation of the dollar • Sub-prime mortgage, credit crunch • Fed lowered discount rate

  7. Trends in Inflation

  8. Methodologies • Loss generation model • Loss decay model • Inflation model • Ornstein-Uhlenbeck • Real interest rate model • 2 factor Hull-White • Fixed claim model • D’Arcy & Gorvett

  9. Loss Generation Model • Nominal values: • Normally generated losses compounded by the nominal interest rate • Economic values: • Nominal losses discounted by the inflation rate

  10. Fixed Claim Model

  11. Fixed Claim Model • Discrete approximation of continuous function • Impact of inflation on fixed claim model • ICA

  12. Demonstration • Demo of model

  13. Results • Constant (Case A) vs. stochastic real interest rate (Case B)

  14. Results • Taylor method (Case B) vs. Fixed claim model (Case C, base case)

  15. Results • Impact of time step: monthly (Case D)

  16. Results • Periods of high & volatile inflation (Case E)

  17. Summary • Traditional loss reserving methods do not reflect the economic value of loss reserves • Economic value ranges are smaller than the nominal value ranges

  18. Sensitivity Analysis • Sensitivity of results from adjusting the number of claims and number of simulations

  19. Feedback • Decoupling of nominal interest rate and inflation • Observed correlation was ~80-90% • From assignment 1… • Correlation between nominal interest rate and inflation was ~40% • New model controls for correlation

  20. Feedback • ALM • Companies do not fully duration match their liabilities • Duration matching sacrifices yield • Impact of duration-mismatch on reserves • Outside scope of research

  21. Feedback • Fisher Formula in a short-rate, stochastic modeling context • Found it to be appropriate • CPI as a proxy for claims inflation not appropriate • Masterson claims cost index

  22. Feedback • Discrepancies in results with different time steps • Indication of improper discretization • Use monthly time step

  23. Ongoing work… • Incorporation of suggestions • Changes the results • Economic value CI becomes larger than nominal value CI • Changes supporting motivation of smaller reserve ranges

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