Barnett & Zehnwirth

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  1. Extended link ratio family
    • Assumes heteroscedastic normality
    • Standard link ratio model carry assumptions not usually satisfied by data
    • E(y|x) = bx
    • Diagnostic test - wtd stadardized residuals vs fitted value should appear rdm
    • Downward trend indicated that large values are overpredicted and small values are underpredicted
  2. Statistical modeling framework
    • Possibility of parameters in:
    • Acc yr - determines level from yr to yr
    • Dvpmt yr - orthogonal to acc yr
    • Pmt yr - trend from pay yr to pay yr
    • median = exp(α + Σγk)
    • mean = median * exp(0.5σ²)
  3. Statistical Modeling: Assumptions about future
    • If pmt / CY trend has been stable in the more recent yrs, assumptin relatively straightforward
    • If unstable, assumptions about future will depend on explanation for the instability
  4. Statistical Modeling: prediction intervals
    • In an insr writes more than one long-tail line and aims for a 100(1 - α)% security level on all the lines combined, then the risk margin per line decreases the more lines the company writes.
    • Let se = standard error and rm = risk margin:
    • se(Total) = √[se²(1) + ... + se²(n)]
    • if rm(all lines) = k*se(Total) then
    • rm(j) = k*se(j)/Σse(i) < k*se(j)
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Barnett & Zehnwirth
Exam6 by Esaie Barnett & Zehmwirth
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