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Examples
Consider an NCD scheme with three levels of premium
discount: 0%, 25% and 50%. The undiscounted
premium is $9000. If a policyholder makes no claims
during the year, he/she moves up one level (or stays at
the highest level). Otherwise, if a claim is made, he/she
moves down a level (or stays at the lowest level). A
policyholder only makes a claim if they have an accident
that leads to a loss of more than $50. A policyholder will
have at most one accident per year, with probability
1
2
e
0
.
25
. Given that an accident occurs, the loss is
exponentially distributed with mean $200.
1.
Determine the transition matrix for this scheme.
2.
What is the probability that a new policyholder is in
the 50% class in 2 years’ time?
3.
Determine the longrun proportions within each
level of the NCD scheme and hence the average
premium paid by a policyholder in the long run.
UNSW Week 9 ACTL1001 Tutorial
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Transition Matrix
Given that a loss occurs, the probability that the loss is greater
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 One '09
 Nicole

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