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
