Brosius

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Esaie
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33874
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Brosius
Updated:
2010-09-10 17:25:32
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Exam6 by Esaie
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Exam6 by Esaie Brosius
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  1. Link ratio, budgeted loss, least square
    • Link ratio: L(x) = cx
    • where c = y/x
    • Budgeted loss: L(x) = k
    • Least square: L(x) = a + bx
    • where b = (xy-x*y)/(x² - (x)²) and a = y - bx
  2. Hugh White's Questions
    • If rpt loss is greater than expected, do you
    • Reduce bulk reserve by corresponding amt (BL)
    • Leave bulk reserve a same % of exp loss (BF)
    • Increase bulk in proportion (LR)
  3. Loss reporting distributions
    • X = rpt nb clm, Y = ult nb clm
    • Q(x) = E(Y|X = x)
    • R(x) = E(Y - X|X = x)
  4. Poisson-Binomial distribution
    • Poisson(μ), Binomial(r,δ)
    • Q(x) = x + μ(1 - δ)
    • R(x) = μ(1 - δ)
    • BF is optimal in this case
    • Note: no answer optimal for Neg Bin
  5. LS: Poisson-Binomial Case
    • Poisson(μ), Binomial(r,δ)
    • Q(x) = x + μ(1 - δ)
    • R(x) = μ(1 - δ)
    • BF is optimal in this case
    • Note: no optimal case for Neg Bin
  6. When is least square method appropriate
    • If yr to yr chg are due largely to systematic shifts in the book of business, other methods may be more appropriate
    • If rdm chance is the primary cause of flucuations, the least square should be considered
  7. Lest square cred dvpt formula
    • L(x) = Z(x/d) + (1 - Z)E(Y)
    • Z = VHM / (VHM + EVPV)
    • VHM = Var(dY) = d²V(Y)
    • EVPV = E(Var(X/Y)*Y²)
  8. Least square dvpt conclusions
    • When rdm yr to yr fluctuations are severe, least square tends to produce more reasonable estimates of ultimate than link ratio
    • Does not require a great deal of additional data
    • Works best when used w. understanding of its limitations
    • When significant exposure chgs, can go astray unless make necessary chgs
    • Subject to sampling errors due to parameters estimation
    • Can be helpful in developing losses for small states or for lines subject to serious fluctuations

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