Venter Factors Flashcards
what does Venter focus on (compared to Mack)?
Venter Factors
focuses on predicting incremental losses rather than cumulative losses
what is the first assumption of Mack?
Venter Factors
expected value of incremental losses to emerge in next period is proportional to the total losses emerged to date, by AY, assumes f(d) is constant across AY
what is the second assumption of Mack?
Venter Factors
AY are independent
what is the third assumption of Mack?
Venter Factors
variance of the next increment is a function of the age and cumulative losses to date
if future loss emergence is a constant plus a percent of emergence to date, what development should be used?
(Venter Factors)
a factor plus constant development
if future loss emergence is proportional to ultimate losses rather than to emerged to date, what approached is preferred?
(Venter Factors)
Bornhuetter/Ferguson
what are testable implications of the CL assumptions?
Venter Factors
- significance of factor f(d)
- superiority of factor assumption to alternative emergence patterns
- linearity of model
- stability of factor
- no correlation among columns
- no high or low diagonals
what alternative emergence patterns can the CL method be compared against?
(Venter Factors)
-linear with constant (f(d)c(w,d) + g(d))
-factor times parameter (f(d) * h(w))
-including CY effect
(f(d)h(w)*g(w+d))
how to test the linearity of the CL model?
Venter Factors
look at residuals as a function of c(w,d)
how to test the stability of factors in the CL model?
Venter Factors
look at residuals as a function of time
what is a general rule for testing the significance of factors?
(Venter Factors)
absolute value of a factor f(d) is required to be at least twice its SD to be considered significantly different from zero
how can a strict statistical test for the significance of a factor be formed?
(Venter Factors)
if distribution of factor is known - normal is fine, but positive skewness is often observed, so lognormal distribution may be more appropriate
if f(d) predicts cumulative losses rather than incremental losses, how do we test the significance of the factor?
(Venter Factors)
test the significance of the difference of the factor from 1
what test statistic do we use to test CL superiority to alternative emergence patterns?
(Venter Factors)
use SSE, adjusted for number of parameters used:
SSE / (n-p)^2
how is n defined in the SSE adjustment for parameters?
Venter Factors
number of predicted points in the paper - exclude the first column, as it is assumed to be given
what is the effect of using more parameters in CL model?
Venter Factors
advantage in fitting, but disadvantage in prediction
what are alternative test statistics to use when testing CL superiority to other emergence patterns?
(Venter Factors)
AIC = SSE * exp(2p/n) BIC = SSE * n^(p/n)
what is a drawback of the Akaike Information Criteria?
Venter Factors
tends to overparameterize large data sets
what does alt. emergence pattern 2 state? (factor times parameter)
(Venter Factors)
states that next period’s expected emerged loss is a lag factor f(d) times the expected ult. loss amount h(w) for an AY
how many parameters does alt. emergence pattern 2 use (parameterized BF model)?
(Venter Factors)
for complete triangle with m AY, model has 2m-2 params (twice as many as CL)
how can we reduce the number of parameters in the BF model?
Venter Factors
- full model assumes AY ult. losses are at different mean levels, each age has a different percentage of ult. losses
- instead assume several AY in row have same mean level
- assume subsequent periods all have the same expected percentage dev.
what are other methods of reducing the number of BF params?
Venter Factors
-fit trend line through BF ult. loss params (uses just two AY params)
OR
-group years using apparent jumps in loss levels, fit an h to each group
what is a special case of the BF method?
Venter Factors
CC method - sets h(w) = h, requires same number of params as CL method
what would a factor-only model (no constant) show when graphing age d+1 loss against age d loss?
(Venter Factors)
roughly a straight line through the origin with slope equal to the dev. factor
