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UNSW
ACTL1001 Actuarial Studies and Commerce
Tutorial Exercises 9
Exercise 1
An insurance company allows the following NCD levels
NCD Level Discount %
0
0
1
30
2
50
If a policyholder has no claims in a year then they move to the next higher
level of discount (unless they are already on the highest level, in which case
they stay there). If a policyholder has one or more claims in a year then
they move to the next lowest level of discount (unless they are already on the
lowest level, in which case they stay there). The number of claims each year
is assumed to be Poisson
(0
:
1)
.
1. Calculate the probability that a new policyholder will be on the maximum
2. Assuming that the proportions become stable, out of a new group of pol
icyholders what proportion will eventually be paying the full premium?
Exercise 2
Use the following mortality rates
Age
q
x
30
0.00131
31
0.00132
32
0.00133
33
0.00135
34
0.00138
and a 5% p.a. e/ective interest rate to determine
1. the expected present value of the claim payments for a 5 year term
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 One '09
 Nicole

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