B.04.Mahler 3

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Author:
Exam8
ID:
166005
Filename:
B.04.Mahler 3
Updated:
2012-08-14 14:07:35
Tags:
mahler excess loss mixture
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Description:
Workers Compensation Excess Ratios: An Alternative Method of Estimation
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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

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