ASTAM - Written Qs
Loss amounts in 2024 are projected to be r% greater than loss amounts in
2023, but the aggregate deductible remains at 200. Without making any
calculations, determine if the increase in net stop-loss premium from 2023 to
2024 is less than, equal to, or greater than r%. - correct answer ✔If the
aggregate loss increases by r%, then the net stop-loss premium would
increase by more than r%. Because the deductible is not increasing, the
potential aggregate loss amounts that would have been just below the
deductible will increase enough to begin contributing to the expected value.
We can also consider the definition of net stop-loss premium. The limited
expected aggregate loss would increase by less than r% because inflating the
size of aggregate losses above 250 would still only result in a limited loss of
250. Since the limited expected loss has a negative impact on the net stop-
loss premium, the total percentage increase in the net stop-loss premium
would be larger than r%.
Explain two reasons why the non-normal confidence region is better than the
normal confidence intervals. - correct answer ✔The confidence intervals
calculated in part (c) assume that the maximum likelihood estimators are
normally distributed. This assumption is asymptotically true but may not hold
for small samples.
Because the parameter estimates (alpha hat) and (beta hat) are not
independent, a confidence region is better as it accounts for the joint effect,
unlike the confidence intervals calculated in part (c), which treat the
parameters separately.
Briefly discuss if we should discount the outstanding claims reserve. - correct
answer ✔ANSWER 1
Usually, reserves are not discounted. Leaving reserves undiscounted provides
a layer of conservatism. The difference between undiscounted and discounted
reserves can be viewed as an implicit provision for adverse deviation.
, ANSWER 2
Discounting reserves gives the insurer more cash flow to invest with, which
can potentially improve profitability and, in turn, allow the insurer to set more
competitive rates. Thus, discounting reserves is preferable.
Describe one advantage of the Hill estimator compared to the GPD in
estimating S(x). - correct answer ✔Advantage: The Hill estimator is slightly
less complex and does not require the use of parameter beta in estimating
S(x) unlike the GPD (one less parameter).
Describe one disadvantage of the Hill estimator compared to the GPD in
estimating S(x). - correct answer ✔Disadvantage: The Hill estimator is
derived based on the assumption that the underlying loss distribution is in the
Fréchet MDA, i.e., epsilon>0, which might not always be true. Thus, the Hill
estimator will result in a poorer S(x) estimate, especially when the underlying
loss distribution isn't in the Fréchet MDA.
Identify one disadvantage of using a frequency-severity method to estimate
reserves. - correct answer ✔Disadvantage: They require more data than
other reserving methods do.
Identify one advantage of using a frequency-severity method to estimate
reserves. - correct answer ✔Advantage: They allow us to split losses into
frequency and severity, allowing us to make separate assumptions for each.
If the indicated relativities for both loss ratio and loss cost methods are the
same, this means that the distribution of all cross-variables is
_________________________. - correct answer ✔homogeneous
How to propose a suitable threshold given a plot of an empirical MEL function
against ordered losses - correct answer ✔We want the region above the
Loss amounts in 2024 are projected to be r% greater than loss amounts in
2023, but the aggregate deductible remains at 200. Without making any
calculations, determine if the increase in net stop-loss premium from 2023 to
2024 is less than, equal to, or greater than r%. - correct answer ✔If the
aggregate loss increases by r%, then the net stop-loss premium would
increase by more than r%. Because the deductible is not increasing, the
potential aggregate loss amounts that would have been just below the
deductible will increase enough to begin contributing to the expected value.
We can also consider the definition of net stop-loss premium. The limited
expected aggregate loss would increase by less than r% because inflating the
size of aggregate losses above 250 would still only result in a limited loss of
250. Since the limited expected loss has a negative impact on the net stop-
loss premium, the total percentage increase in the net stop-loss premium
would be larger than r%.
Explain two reasons why the non-normal confidence region is better than the
normal confidence intervals. - correct answer ✔The confidence intervals
calculated in part (c) assume that the maximum likelihood estimators are
normally distributed. This assumption is asymptotically true but may not hold
for small samples.
Because the parameter estimates (alpha hat) and (beta hat) are not
independent, a confidence region is better as it accounts for the joint effect,
unlike the confidence intervals calculated in part (c), which treat the
parameters separately.
Briefly discuss if we should discount the outstanding claims reserve. - correct
answer ✔ANSWER 1
Usually, reserves are not discounted. Leaving reserves undiscounted provides
a layer of conservatism. The difference between undiscounted and discounted
reserves can be viewed as an implicit provision for adverse deviation.
, ANSWER 2
Discounting reserves gives the insurer more cash flow to invest with, which
can potentially improve profitability and, in turn, allow the insurer to set more
competitive rates. Thus, discounting reserves is preferable.
Describe one advantage of the Hill estimator compared to the GPD in
estimating S(x). - correct answer ✔Advantage: The Hill estimator is slightly
less complex and does not require the use of parameter beta in estimating
S(x) unlike the GPD (one less parameter).
Describe one disadvantage of the Hill estimator compared to the GPD in
estimating S(x). - correct answer ✔Disadvantage: The Hill estimator is
derived based on the assumption that the underlying loss distribution is in the
Fréchet MDA, i.e., epsilon>0, which might not always be true. Thus, the Hill
estimator will result in a poorer S(x) estimate, especially when the underlying
loss distribution isn't in the Fréchet MDA.
Identify one disadvantage of using a frequency-severity method to estimate
reserves. - correct answer ✔Disadvantage: They require more data than
other reserving methods do.
Identify one advantage of using a frequency-severity method to estimate
reserves. - correct answer ✔Advantage: They allow us to split losses into
frequency and severity, allowing us to make separate assumptions for each.
If the indicated relativities for both loss ratio and loss cost methods are the
same, this means that the distribution of all cross-variables is
_________________________. - correct answer ✔homogeneous
How to propose a suitable threshold given a plot of an empirical MEL function
against ordered losses - correct answer ✔We want the region above the
