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Property-Liability Insurance Loss Reserve Ranges Based on Economic Value

Property-Liability Insurance Loss Reserve Ranges Based on Economic Value. Stephen P. D’Arcy, FCAS, PhD Alfred Y. H. Au, Actuarial Student Liang Zhang, Actuarial Student University of Illinois Casualty Loss Reserve Seminar September 2008

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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 Stephen P. D’Arcy, FCAS, PhD Alfred Y. H. Au, Actuarial Student Liang Zhang, Actuarial Student University of Illinois Casualty Loss Reserve Seminar September 2008 We wish to thank the Actuarial Foundation and the Casualty Actuarial Society for providing financial support for this research.

  2. Overview • Background • Loss reserve ranges • Economic value of loss reserves • Inflation • Methodology • Running the model • Results • Further research • Conclusions

  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. Methodology • Loss generation model • Loss decay model (payment pattern) • Inflation model • Ornstein-Uhlenbeck • Masterson Claim Cost Index • Nominal 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

  12. Running the Model http://www.business.uiuc.edu/~s-darcy/papers/LossReserveRangeModelv2.xls • Input Sheet • Loss Generator • Nominal Interest Rate • Inflation • Inflation under Fixed Claim • Fixed Claim Model • Summary • Masterson Claim Cost Index

  13. Input Sheet

  14. Loss Generator

  15. Nominal Interest Rate

  16. Inflation

  17. Impact of Inflation on Claims

  18. Fixed Claim Model

  19. Summary

  20. Masterson Claim Cost Index

  21. Results Taylor Method vs. D’Arcy-Gorvett Approach

  22. ResultsHigher Claim Cost Inflation

  23. ResultsHigher Inflation/Interest Rate Correlation

  24. ResultsHigher and More Volatile Inflation

  25. Further Research • Two factor approach to loss reserving • Deflate loss triangle • Generate reserve ranges on deflated losses • Incorporate inflation variability separately • Useful when inflation rate or variability changes • Available at: http://www.business.uiuc.edu/~s-darcy/ • ALM issues • Some companies intentionally mismatch assets and liabilities to pick up yield • Mismatching would increase the risk of an increase in inflation

  26. Summary • Traditional loss reserving methods do not reflect the economic value of loss reserves • Economic value ranges can be smaller than the nominal value ranges • Results are more significant during periods of high inflation rates and increased inflation volatility

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