Clark

Question 1

what are two objectives in creating a formal model of loss reserving?

(Clark)

Answer 1

• describe loss emergence in simple mathematical terms as a guide to selecting amounts for carried reserves
• provide a means of estimating the range of possible outcomes around the expected reserve

Question 2

what are two key elements of a statistical loss reserving model?

(Clark)

Answer 2

• expected amt of loss to emerge in some time period

- distribution of actual emergence around the expected value

Question 3

a model will estimate the expected amt of loss to emerge based on what two quantities?

(Clark)

Answer 3

• estimate of ult loss by year

- estimate of pattern of emergence

Question 4

what is assumed about the loss emergence pattern when using the loglogistic or weibull curves?

(Clark)

Answer 4

assume a strictly increasing pattern

Question 5

what are three advantages to using parameterized curvers to describe the emergence pattern?

(Clark)

Answer 5

• estimation is simple (only two parameters)
• can use data from an unevenly spaced triangle
• final pattern is smooth and doesn’t follow random movements in historical age-to-age factors

Question 6

what does the LDF method assume about loss amt in each AY?

Clark

Answer 6

assumes loss amt in each AY is independent from all other years

Question 7

what does the CC method assume about the loss amt in each AY?

(Clark)

Answer 7

assumes there is a known relationship between expected losses across AY, where the relationship is identified by an exposure base (prem @ CRL, sales, payroll, etc.)

Question 8

which is preferred, the CC or LDF method?

Clark

Answer 8

CC - data is summarized into a loss triangle with relatively few data points

Question 9

what is a drawback of the LDF method?

Clark

Answer 9

requires estimating a number of parameters - tends to be overparameterized when few data points exist

Question 10

how do the parameter variances of the CC and LDF methods compare?

(Clark)

Answer 10

CC has smaller param variance (additional info from exposure base + fewer params)

Question 11

what is process variance? (wrt variance of actual loss emergence)

(Clark)

Answer 11

the “random” amt

Question 12

what is parameter variance?
(wrt variance of actual loss emergence)

(Clark)

Answer 12

the uncertainty in the estimator, aka estimation error

Question 13

what are key advantages of using the over-dispersed Poisson distribution to model process variance?

(Clark)

Answer 13

• inclusion of scaling factors allows us to match first and second moments of any distribution -> high flexibility
• MLE produces the LDF and CC estimates of ult losses, so results can be presented in a familiar format

Question 14

what is an advantage of using the MLE function?

Clark

Answer 14

works in the presence of negative or zero incremental losses

Question 15

what are three key assumptions of the Clark model?

Clark

Answer 15

1 - incremental losses are IID
2 - variance/mean scale parameter sigma^2 is fixed and known
3 - variance estimates are based on an approximation to the Rao-Cramer lower bound

Question 16

how can the independence assumption of the Clark model be tested?

(Clark)

Answer 16

-using residual analysis to notice positive/negative correlation

Question 17

what might cause positive correlation between accident periods?

(Clark)

Answer 17

change in loss inflation that equally impacts all periods

Question 18

what might cause negative correlation between accident periods?

(Clark)

Answer 18

large settlement in one period replaces a stream of payments in later periods

Question 19

why do we use the Rao-Cramer lower bound to estimate variance?

(Clark)

Answer 19

-estimate of variance based on information matrix is only exact when using linear functions, but our model is non-linear

Question 20

how do we calculate the process standard deviation of the reserves for an AY?

(Clark)

Answer 20

multiply the scale parameter sigma^2 by the estimated reserves, then take the square root

Question 21

what might we plot residuals against to test model assumptions?

(Clark)

Answer 21

• increment age (i.e. AY age)
• expected loss in each increment
• accident year
• calendar year

Question 22

what does plotting residuals against expected loss in each increment test?

(Clark)

Answer 22

tests if variance/mean ratio is constant

Question 23

what does plotting residuals against calendar year achieve?

Clark

Answer 23

tests diagonal effects

Question 24

how do we test the constant ELR assumptions in the Cape Cod model?

(Clark)

Answer 24

graph ult. loss ratios by AY.
ULR = reported losses / used-up premium
-if increasing or decreasing pattern exists, assumption may not hold

Question 25

why would we use Clark’s model to calculate the 12-month development?

(Clark)

Answer 25

estimate is testable within a short timeframe - can compare it to actual development and see if it was within the forecast range

Question 26

what other calculations are possible with Clark’s model?

Clark

Answer 26

• variance of prospective losses
• calendar year development
• variability in discounted reserves

Question 27

why is the coefficient of variation lower for discounted reserves?

(Clark)

Answer 27

tail of the payout curve has the greatest parameter variance and also receives the deepest discount

Question 28

why wouldn’t we use the CV from Clark’s model when selecting a reserve other than the MLE?

(Clark)

Answer 28

the estimate of SD in the MLE model is directly tied to the MLE

Question 29

why might we use the CV from Clark’s model when selecting a reserve other than the MLE?

(Clark)

Answer 29

final carried reserve is a selection, so the SD can also be a selection. output from the MLE model is a reasonable basis for that selection

Question 30

why are the weibull and loglogistic growth curves good for Clark’s model?

(Clark)

Answer 30

• smoothly move from 0% to 100%
• closely match empirical data
• first and second derivatives are calculable

Question 31

what is the main conclusion of Clark’s paper?

Clark

Answer 31

-parameter variance is generally larger than the process variance -> our need for more complete data (e.g. exposure data in CC) outweighs need for more sophisticated models