Brosius

Question 1

Least squares method, formula for L(x), a, and b

Answer 1

Question 2

link ratio method

Answer 2

a=0

L(x)=cx=x/d

use if a<0 becuase y is negative for small values of x

if you decide to switch to link ratio method, need to calculate c and not use b

Question 3

budgeted loss method

Answer 3

b = 0

L(x) = mean(y)

if b<0, use budgeted loss method

Question 4

B-F

Answer 4

b=1

Question 5

where do LSM, link, and budgeted intersect

Answer 5

(mean(x), mean(y))

Question 6

what is advantage of least squares

Answer 6

Flexibility is advantage since it gives more or less weight to observed value of x as appropriate

Question 7

Hugh White’s question: trying to establish reserve and reported portion of expected losses as of statement date for current AY is 8% higher than it “should” be

Answer 7

• reduce bulk reserve -> budgeted loss
• leave bulk reserve at same % level of expected losses -> BF
• increase bulk reserve in proportion to increase of actual reported over expected reported -> link ratio
• all 3 methods are reasonable

Question 8

shortcut for c

Answer 8

mean(y)/mean(x)

Question 9

if prem given

Answer 9

calculate LR then apply least squares method

Question 10

why is it difficult to compute pure Bayesian estimate Q

Answer 10

requires knowledge of loss and loss reporting processes

Question 11

why is best linear approx a good replacement to Bayesian?

Answer 11

simpler to compute

easier to understand and explain

less dependent on underlying dist

Question 12

L is best linear approx to Q

L is linear function that minimizes

Answer 12

Ex[(Q(X)-L(X))²]

Question 13

development formula 1

Answer 13

L(x)=(x-EX)*COV(X,Y)/Var(X) + E[Y]

Question 14

answers to Hugh when using DF1

Answer 14

-if COV<var></var>

<p>-if COV=Var, large reported amnt should not affect reserve aka BF</p>

<p>-if COV&gt;Var(X), should lead to increase in reserve aka link ratio</p>

</var>

Question 15

when is LSM appropriate and not appropriate

Answer 15

• LSM is appropriate when year to year fluctuations are random
• Not appropriate if year to year changes in loss experience are due largely to systematic shift or distortions in BoB
• if systematic distortions (inflation, growing book), data can be adjusted before applying LSM

Question 16

Credibility form of development formula AKA DF2

Answer 16

configure DF1 into credibility weighting system

L(x)=Z*x/d+(1-Z)*E[Y]

Z=VHM/(VHM+EVPV)

credibility weighting of link ratio estimate x/d and budgeted E[Y]

EVPV = 0 when full weight to link ratio (fixed reporting)

VHM = 0 when full weight to budgeted (fixed prior)

Question 17

VHM and EVPV

Answer 17

Year to year changes in loss and loss reporting distributions are too large to be corrected for -> need to estimate EVPV and VHM

Question 18

other formula for Z

Answer 18

Z=bd=b/c

Question 19

caseload effect/what DF2 assumes

Answer 19

• DF2 assumes that expected # of claims reported is proportional to # of claims incurred
• when caseload is low, claim is more like to reported quickly so development ratio is expected to be decreasing fct of y not constant
• DF3: E[X/Y|Y]=d -> d+xo/y

Question 20

caseload effect -> how to calculate

Answer 20

E[X|Y=y]=dy+x0

have 2 equations -> considering new legislation and considering resouce constraints

solve for d and x0

calc VHM and EVPV as normal ie dont alter E[X/Y] and E[Y] (use considering new legislation values)

calc Ult using DF3 (use x0 and d)