Brosius
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Author:
Esaie
ID:
33874
Filename:
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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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
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)
Loss reporting distributions
X = rpt nb clm, Y = ult nb clm
Q(x) = E(Y|X = x)
R(x) = E(Y - X|X = x)
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
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
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
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)
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