Hi, The solution to Question 14.2 (i) (page 27) mentions several specific quantitative assertions:
"Suppose that the distribution of liability outgo approximates a normal distribution (or something with similar dispersion). We would therefore be very sure that the liability outgo will not exceed $130 million, ie three standard deviations above the expected value (around 99.9% sure).
We have no measure of the uncertainty of the premium income. However, it would be imprudent to rely upon the full $100 million. Assuming that the company’s trading policy for the next year was not under threat of some radical plan (eg to stop writing business) then it would probably be safe to rely upon, say, $80 million. On the basis of these figures, we would be exceedingly surprised if $50 million in money market investments was insufficient."
Where do these assertions (3 standard deviations, $80mn, $50mn) come from and are they a subjective example view or a reliable actuarial judgement which should be used in other questions?
"Suppose that the distribution of liability outgo approximates a normal distribution (or something with similar dispersion). We would therefore be very sure that the liability outgo will not exceed $130 million, ie three standard deviations above the expected value (around 99.9% sure).
We have no measure of the uncertainty of the premium income. However, it would be imprudent to rely upon the full $100 million. Assuming that the company’s trading policy for the next year was not under threat of some radical plan (eg to stop writing business) then it would probably be safe to rely upon, say, $80 million. On the basis of these figures, we would be exceedingly surprised if $50 million in money market investments was insufficient."
Where do these assertions (3 standard deviations, $80mn, $50mn) come from and are they a subjective example view or a reliable actuarial judgement which should be used in other questions?