General Insurance Spring Seminar

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General Insurance Spring Seminar

• Friday 21 May 2004, Staple Inn Hall

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Reserve Ranges Stochastic Reserving

• 1. Background
• 2. Thomas Mack Method
• 3. Multi-Line
• 4. Alternative Practical Approach

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Ranges in Practice

• Percentages
• Varying Parameters
• Stochastic

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Stochastic Methods Problems

• To match deterministic model
• BF methodology
• Incurred claims redundancy
• Spurious data
• Tail
• Multi-lines/correlation
• Large losses
• Latent claims

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Stochastic v DeterministicNot same mid-point

• Use range unchanged
• Move range
• Pro-rata adjustment

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Thomas Mack MethodAssumptions

• Independence of accident years
• E(Ci,k1Ci1,Cik) Cikfk
• Var(Ci,k1Ci1,Cik) Cik?k2

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Mack Adjustments

• Alternative development factors
• Omit data cells
• By year to give correct overall result
• BF
• Tail

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Formulae

• Standard error by accident year given by

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Formulae last s.e.

• Given by

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Formula Overall Standard Error

• Standard error overall and adjustment given by

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Formula Tail Factor Adjustment

• Tail factor adjustment given by

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BF A Priori Loss Ratio VariabilityChoices

• Time Series
• Rate/Inflation Adjusted

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BF as Credibility FormulaFormula for standard
error

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Multi-Line

• Correlation between classes
• Use _at_Risk and Correlation Matrix
• Paper gives simple alternative basic copula

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Chain-Ladder Practical Alternative

• Follow deterministic method
• Standard errors based on selected/alternative
  development factors
• Use _at_Risk to complete triangle
• Allow for correlation where appropriate
• Part-year triangles/large losses/omit cells etc.
• BF adjustment as above

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Graph of Results