# B.04.Mahler 3

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1. Mahler alternative method of estimating R(L)
• use direct calculation at low limits
• use a fitted curve at higher limits
• mean residual life (MRL): \$ expected XS of L given claim > L
2. Steps to combine R(L) data
• truncate at d
• Fy(x) = 0 if x ≤ d
• Fy(x) = Fx(x) - Fx(d) / (1 - Fx(d)) otherwise
• shift to zero: Fw(x) = Fy(x+d)
• normalize to achieve mean unity
3. Mahler's mixture
• mixture of Pareto A(x;s,b) & exponential B(x;c)
• Pareto: cdf = 1 - (1 + x/b)-s
• Exponential: cdf = 1 - e-x/c; R(r) = e-r
• F(x;s,b,c) = pA(x) + (1-p)B(x)
• RF(L) = [pmARA(L) + (1-p)mBRB(L)\ / [pmA - (1-p)mB]
• (+) R(L) closer fit (influenced by 4 parameters)
• (+) for mid-lvl values, steady drop off similar to exponential, and pareto keeps R(L) from deteriorating too quickly at high values
• R(L), L>d = (base using data) * R(hat)(L - d)
4. Truncation point
• low enough to have enough data to fit reasonable curve
• high enough that it provides a reasonable ballast to the base factor
 Author: Exam8 ID: 166005 Card Set: B.04.Mahler 3 Updated: 2012-08-14 18:07:35 Tags: mahler excess loss mixture Folders: Description: Workers Compensation Excess Ratios: An Alternative Method of Estimation Show Answers: