# B.9. Mahler 3 - WC XS Ratios

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1. Excess Loss Factor
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)
• 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

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 Author: EExam8 ID: 306706 Filename: B.9. Mahler 3 - WC XS Ratios Updated: 2015-09-11 13:09:59 Tags: Mahler Workers Compensation WC XS Excess Ratio Folders: Description: Mahler 3 - Workers Compensation Excess Ratios Show Answers:

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