B.8. Mahler 2 - Retrospective Rating

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  1. Phenomena affecting excess ratios:
    • different sizes of claims may have varying expected amounts of development
    • dispersion effect: even losses of the same size might develop differently
  2. Simple Dispersion
    • R(L) = weighted avg of XS ratios
    • Ei(X) = expected value of X between xi and xi+1
    • R(L) = ∑Ri(L)Ei(X) / E(X)
    • Rhat(L)= ∑piriR(L/ri) / ∑piri
    • this allows the severity curve to have different distributions in different parts of the curve
    • conclusion: even if losses develop by a factor of 1 on average, the probability of developing higher/lower actually affects R(L) if the severity distribution isn't constant
  3. Generalized Dispersion
    • F(y)=∫0 to ∞ D(y/r) h(r) dr
    • if losses ~ exponential, and loss divisors ~ gamma, developed losses ~ Pareto
    • increasing the shape parameter of a Pareto distribution decrease tail and variance
    • we can use piece-wise linear distribution to estimate distribution in pieces and then weight
    • dispersion increases when loss divider has a heavier tail (e.g. gamma)
    • dispersion increases when coefficient of variation of the loss divisor distribution increases
    • greater dispersion results in greater excess ratios

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B.8. Mahler 2 - Retrospective Rating
2015-09-10 11:29:56
Mahler Retrospective Rating

Mahler 2 - Discussion of Retrospective Rating
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