# 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
 Author: Esaie ID: 33874 Card Set: Brosius Updated: 2010-09-10 21:25:32 Tags: Exam6 by Esaie Folders: Description: Exam6 by Esaie Brosius Show Answers: