Mack (1994) Flashcards
why are confidence intervals appealing? (3)
Mack - 1994
- estimated ult. claims are not an exact forecast of true ult. claims
- allows inclusion of business policy (i.e. management philosophy) by using a specific confidence probability
- allows comparison between CL and other reserving procedures
what implicit assumption does the CL method make? (first assumption)
(Mack - 1994)
assumes that the info used in C_i,I+1-i cannot be augmented by using other C_ik
(i.e. C_i,I+1-i serves as the only basis for the projection to ultimate)
what is a consequence of the first implicit assumption of the CL method?
(Mack - 1994)
assumes development factors are uncorrelated
-expected f_k is the same, despite high or low previous development
what is the second implicit assumption of the CL method?
Mack - 1994
assumes AYs are ind’pt
what is a major consequence of the second implicit assumption of the CL method?
(Mack - 1994)
CL method cannot be used for triangles where CY effects (e.g. change in claims handling or case reserving) affect several AY in the same way
why do we use a weighted average for f_k instead of a simple average?
(Mack - 1994)
weighted avg provides a smaller variance for f_k
what is the third implicit assumption of the CL method?
Mack - 1994
Var(C_j,k+1 | C_j1,…,C_jk) = C_jk * alpha_k^2
where alpha_k^2 is an unknown proportionality constant
what are our options for an estimator for alpha_I-1?
Mack - 1994
- set equal to 0
- extrapolate series alpha_1, alpha_2, …, alpha_I-2 using loglinear regressions
- set alpha_I-1^2 = min[alpha_I-2^4 / alpha_I-3^2, min(alpha_I-3^2, alpha_I-2^2)]
when should we set alpha_I-1^2 equal to 0?
Mack - 1994
if f_I-1 =1 and claims development is expected to be finished after I-1 years
what are 2 potential problems when using the normal distribution as an approximation to the true distribution of R_i?
(Mack - 1994)
- if data is skewed, it’s a poor approximation
- C.I. can have negative lower limits, even if negative reserve isn’t possible
how do we solve potential issues with using the normal distribution for R_i?
(Mack - 1994)
use lognormal
why is the square of the standard error of R not simply the sum of each (s.e.(R_i))^2?
(Mack - 1994)
R_i are not independent, because each estimator of R_i is influenced by the same age-to-age factor
how are the lower/upper empirical limits calculated?
Mack - 1994
applying the minimum/maximum age-to-age factors for each dev. period to the incurred losses
what are three attempts at finding the f_k that minimizes the weighted sum of squared differences between actual results and fitted results?
(Mack - 1994)
- f_k0 = C_ik^2 weighted avg of individual dev. factors
- f_k1 = C_ik-weighted avg of individual dev factors (usual age-to-age)
- f_k2 = unweighted (simple) average of individual dev. factors
what do f_k0 and f_k2 assume & what is a consequence?
Mack - 1994
assume that Var(C_i,k+1 | C_i1, … , C_ik) is proportional to 1 and C_ik^2 -> this violates third implicit assumption of CL method
what is a benefit of using a regression framework?
Mack - 1994
allows us to check the underlying CL assumptions, including linearity (first implicit assumption) and variance assumption (third implicit assumption)
how do we check the linearity (first implicit) assumption of the CL method?
(Mack - 1994)
plot C_i,k+1 against C_ik in order to see if we have an approximately linear relationship around a straight line through the origin, with slope f_k = f_k1
how do we check the variance (third implicit) assumption of the CL method?
(Mack - 1994)
-plot weighted residuals against C_ik in order to see if the residuals appear random
what weighted residuals would we plot against C_ik to test the variance assumption of the CL method?
(Mack - 1994)
Plot 0: (C_i,k+1 - C_ikf_k0) against C_ik
Plot 1: (C_i,k+1 - C_ikf_k1)/sqrt(C_ik) against C_ik
Plot 2: (C_i,k+1 - C_ik*f_k2)/C_ik against C_ik
if Plot 0 or 2 appears more random than Plot 1, consider replacing f_k1 = f_k with f_k0 or f_k2
how do we check that subsequent development factors are uncorrelated?
(Mack - 1994)
use a test procedure based on Spearman’s rank correlation coefficient
when is the second implicit assumption of the CL method broken?
(Mack - 1994)
when we have CY influences that affect multiple AY
what are examples of CY influences?
Mack - 1994
- reserve strengthening/weakening
- changes in payment processes
- changes in inflation
