# Brosius

 Link ratio, budgeted loss, least square Link ratio: L(x) = cxwhere c = y/xBudgeted loss: L(x) = kLeast square: L(x) = a + bxwhere b = (xy-x*y)/(x² - (x)²) and a = y - bx Hugh White's Questions If rpt loss is greater than expected, do youReduce 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 clmQ(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 caseNote: 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 caseNote: 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 appropriateIf 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 ratioDoes not require a great deal of additional dataWorks best when used w. understanding of its limitationsWhen significant exposure chgs, can go astray unless make necessary chgsSubject to sampling errors due to parameters estimationCan be helpful in developing losses for small states or for lines subject to serious fluctuations AuthorEsaie ID33874 Card SetBrosius DescriptionExam6 by Esaie Brosius Updated2010-09-10T21:25:32Z Show Answers