Venter

Question 1

Incremental age-to-age factor

Venter

Answer 1

f(d) = incremental loss / prior cumulative loss

Question 2

Tests of loss emergence (2)

Venter

Answer 2

1. significance of factors

2. superiority to alternate emergence patterns

Question 3

Test for significance of factors (and adjustment if measuring cumulative LDFs)
(Venter)

Answer 3

to be significant, a factor should be >= 2x it’s standard deviation

*if age-to-age factors are cumulative, test whether (1 - factor) is significant

Question 4

Tests for superiority of alternate emergence patterns, implication of alternate emergence pattern, and definition of n and p (3)
(Venter)

Answer 4

1. adjusted SSE
2. AIC
3. BIC

*implies that the linearity assumption fails

n = # predicted points (= # cells less 1st column)
p = # parameters

Question 5

Adjusted SSE formula

Answer 5

adjusted SSE = SSE / (n - p)^2

Question 6

AIC formula

Venter

Answer 6

AIC = SSE * exp(2p / n)

Question 7

BIC formula

Venter

Answer 7

BIC = SSE * n^(p / n)

Question 8

Alternate emergence patterns (2)

Answer 8

1. linear w/constant - expected incremental loss in next period given data to date = f(d) * cum loss to date + g(d)
   » g(d) = avg incremental loss for age
2. factor * parameter - expected incremental loss in next period given data to date = f(d) * h*(w)

Question 9

Loss emergence from linearity assumption

Answer 9

expected incremental loss in next period given data to date = f(d) * cum loss to date

Question 10

Number of parameters in the CL, BF, and CC methods

Venter

Answer 10

CL = #AYs - 1
BF = 2 * (#AYs - 1)
CC = same as CL

Question 11

f(d) in CL vs. BF/CC methods

Venter

Answer 11

CL: f(d)’s are link ratios

BF/CC: f(d)’s are lag factors (incremental % reported)

Question 12

Explain how the CC method is a reduced parameter version of the BF method

Answer 12

special case that uses h(w) = h (constant AY parameter across AYs)

Question 13

Ways to reduce the number of parameters (4)

Answer 13

1. assume the same AY level across several years
2. assume subsequent development periods have the same % development
3. fit a trend line through BF ultimate loss parameters
4. group AYs with similar levels and fit an h parameters to each group

Question 14

Residual tests (2)
(Venter)

Answer 14

1. linearity of development factors

2. stability of development factors

Question 15

Tests of independence (2)

Venter

Answer 15

1. correlation of development factors *»linearity test in Mack
2. significantly high or low diagonals (CY effects)

Question 16

Lags (% emerged)

Answer 16

lag = incremental age-to-age factor / cumulative age-to-ultimate

= incremental % emergence

Question 17

Fitted h(w) parameters for fitting a parameterized BF model

Answer 17

h(w) = sum across row (incremental claims * lag) / sum across row (lag^2)

Question 18

Fitted f(d) parameters for fitting a parameterized BF model

Answer 18

f(d) = sum down col (incremental claims * h(w)) / sum down col (h(w)^2)

Question 19

Weighted least squared iterated parameterized BF model and when to use it

Answer 19

*use w/o constant variance of residuals

h(w)^2 = sum across row [(incremental claims^2) / lag] / sum across row (lag)

f(d)^2 = sum down col [(incremental claims^2) / h(w)] / sum down col (h(w))

Question 20

Adjustment to h(w) parameter when fitting a parameterized CC

Answer 20

single h value summed across all AYs

Question 21

Residual test for linearity

Venter

Answer 21

plot raw residuals against previous cumulative losses for a given age

> > strings of positive and negative residuals in a row indicate a non-linear process

Question 22

Types of tests for stability of development factors (3)

Venter

Answer 22

1. residuals against time (AY) - strings of positive and negative residuals in a row indicate instability
2. plot a moving average of a specific age-to-age factor - shifts in level over time indicates instability
3. state-space model - compares degree of instability around mean to instability in mean itself over time

Question 23

Adjustments to make if development factors are unstable (2)

Answer 23

1. select a weighted average giving more weight to more recent years
2. adjust triangle (ex: Berquist Sherman)

Question 24

Venter’s test for correlation of development factors

Answer 24

calculates sample correlation (covariance (x,y) / std. dev(x) * std. dev(y)) for all pairs of columns and counts how many are significant using a T-statistic

T = r * [ (n - 2) / (1 - r^2) ]^.5
n = # items compared 

Reject null (no correlation) if absolute value (T) > t-statistic with n-2 df

Question 25

Interpretation of significance level in Venter’s test for correlation of development factors (= AY independence)

Answer 25

acceptable % of column pairs that could be correlated by random chance

Question 26

Test for significantly high or low diagonals (CY effects)

Venter

Answer 26

create a regression matrix

• first column = incremental losses starting w/2nd column
• subsequent columns (one for each age) = previous cumulative losses that inform the incremental losses in column #1
• dummy columns = 1s or 0s to indicate if the loss is on diagonal (skip first diagonal)

> > if dummy column coefficients are significant, assume there are significant CY effects

Question 27

Adjustment to test for CY effects if using CC or additive CL methods

Answer 27

use 0s/1s in cumulative loss columns instead of cumulative losses

Question 28

Threshold for acceptable number of correlated column pairs (Venter)

Answer 28

Threshold = % significance * m + sqrt(m)

Where m = # of column pairs tested.