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Published byEthan Spencer Modified over 9 years ago
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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 Deterministic Not same mid-point: Use range unchanged Move range Pro-rata adjustment
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Thomas Mack Method Assumptions: Independence of accident years E(C i,k+1 |C i1,…C ik ) = C ik f k Var(C i,k+1 |C i1,…C ik ) = C ik k 2
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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 Variability Choices: Time Series Rate/Inflation Adjusted
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BF as Credibility Formula Formula for standard error:
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Multi-Line Correlation between classes Use @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 @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
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