Venter Flashcards
Incremental age-to-age factor
Venter
f(d) = incremental loss / prior cumulative loss
Tests of loss emergence (2)
Venter
- significance of factors
2. superiority to alternate emergence patterns
Test for significance of factors (and adjustment if measuring cumulative LDFs)
(Venter)
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
Tests for superiority of alternate emergence patterns, implication of alternate emergence pattern, and definition of n and p (3)
(Venter)
- adjusted SSE
- AIC
- BIC
*implies that the linearity assumption fails
n = # predicted points (= # cells less 1st column) p = # parameters
Adjusted SSE formula
adjusted SSE = SSE / (n - p)^2
AIC formula
Venter
AIC = SSE * exp(2p / n)
BIC formula
Venter
BIC = SSE * n^(p / n)
Alternate emergence patterns (2)
- 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 - factor * parameter - expected incremental loss in next period given data to date = f(d) * h*(w)
Loss emergence from linearity assumption
expected incremental loss in next period given data to date = f(d) * cum loss to date
Number of parameters in the CL, BF, and CC methods
Venter
CL = #AYs - 1 BF = 2 * (#AYs - 1) CC = same as CL
f(d) in CL vs. BF/CC methods
Venter
CL: f(d)’s are link ratios
BF/CC: f(d)’s are lag factors (incremental % reported)
Explain how the CC method is a reduced parameter version of the BF method
special case that uses h(w) = h (constant AY parameter across AYs)
Ways to reduce the number of parameters (4)
- assume the same AY level across several years
- assume subsequent development periods have the same % development
- fit a trend line through BF ultimate loss parameters
- group AYs with similar levels and fit an h parameters to each group
Residual tests (2) (Venter)
- linearity of development factors
2. stability of development factors
Tests of independence (2)
Venter
- correlation of development factors *»linearity test in Mack
- significantly high or low diagonals (CY effects)
Lags (% emerged)
lag = incremental age-to-age factor / cumulative age-to-ultimate
= incremental % emergence
Fitted h(w) parameters for fitting a parameterized BF model
h(w) = sum across row (incremental claims * lag) / sum across row (lag^2)
Fitted f(d) parameters for fitting a parameterized BF model
f(d) = sum down col (incremental claims * h(w)) / sum down col (h(w)^2)
Weighted least squared iterated parameterized BF model and when to use it
*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))
Adjustment to h(w) parameter when fitting a parameterized CC
single h value summed across all AYs
Residual test for linearity
Venter
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
Types of tests for stability of development factors (3)
Venter
- residuals against time (AY) - strings of positive and negative residuals in a row indicate instability
- plot a moving average of a specific age-to-age factor - shifts in level over time indicates instability
- state-space model - compares degree of instability around mean to instability in mean itself over time
Adjustments to make if development factors are unstable (2)
- select a weighted average giving more weight to more recent years
- adjust triangle (ex: Berquist Sherman)
Venter’s test for correlation of development factors
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
Interpretation of significance level in Venter’s test for correlation of development factors (= AY independence)
acceptable % of column pairs that could be correlated by random chance
Test for significantly high or low diagonals (CY effects)
Venter
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
Adjustment to test for CY effects if using CC or additive CL methods
use 0s/1s in cumulative loss columns instead of cumulative losses
Threshold for acceptable number of correlated column pairs (Venter)
Threshold = % significance * m + sqrt(m)
Where m = # of column pairs tested.
