# 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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 Author: EExam8 ID: 306705 Filename: B.8. Mahler 2 - Retrospective Rating Updated: 2015-09-10 11:29:56 Tags: Mahler Retrospective Rating Folders: Description: Mahler 2 - Discussion of Retrospective Rating Show Answers:

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