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
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 + Σγ_{k})
mean = median * exp(0.5σ²)
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
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.