B.9. Mahler 3 - WC XS Ratios

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B.9. Mahler 3 - WC XS Ratios
2015-09-11 09:09:59
Mahler Workers Compensation WC XS Excess Ratio

Mahler 3 - Workers Compensation Excess Ratios
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  1. Excess Loss Factor
    Excess Loss Factor = Excess Ratio * PLR + Risk Loading
  2. Initial adjustments to the data
    • develop, trend, adjust for legislative changes
    • groups claims into accidents since ELFs are based on per occurrence limits, not per claim
    • note that this grouping prevents us to look at accident level data by injury type
    • approximation could've been to divide claim level limits by 1.1 (not used)
  3. Additional adjustments for curve fitting
    • combine data for 3rd, 4th and 5th reports
    • truncate and shift data: Y = X - T ⇒ R(L) = RY(L - T)*R(T)
    • normalize the truncated and shifted data for each HG to have a mean of 1
    • → all those adjustments make the 4 HG comparable
  4. Methodology
    • fit a mixture to differentiate loss development at different limits
    • Mahler uses a mix of Exponential (works well just above truncation point) and Pareto (thick tail makes it ideal at very high limits)
    • uses mean residual life ($XS/#XS) to examine tail of severity distribution
    • pick an truncation point (e.g. $100K) under which we rely on the data for values of R(L) vs relying on the fitted curve for limits above
  5. Application to actual data
    • under the truncation point use the data R(L)
    • over we use R(L) = Rdata(Ltrunc) * Rfit([X - trunc]/Y])
    • Y = avg value of truncated and shifted losses
    • Rfit(L) = ∑ pjEj(X)Rj(L) / ∑ pjEj(X)
    • Rfit(L) = weighted avg of R(L) using pjEj(X) / ∑ pjEj(X)
  6. Selection of a truncation point
    • permit the maximum reliance on reported data
    • retain enough data above the truncation point to permit reasonable fittingd
    • in general, should be a round number prior to the "thinning out" of the data