Homework Assignment 22:
(1) Do Exercise 14.5 on page 462.
(In part (b), the “first method” refers to the approximation we developed
in class.)
(2) Consider a group life insurance contract with an accidental death benefit.
Assume that for all members
the probability of death in the next year is .01 and that 30% of the deaths are accidental.
For 50
employees the benefit for an ordinary death is 50,000 and for an accidental death it is 100,000.
For the
remaining 25 employees the benefits are 75,000 and 150,000.
What compound Poisson distribution
would be used for approximating the individual model? (Ans
λ
= 0.75, p(50,000) = 0.4667, p(75,000) =
0.2333, p(100,000) = 0.2000, p(150,000) = 0.1000)
(3) An life insurance company has a portfolio of independent risks as shown below:
Class
Probability of a Claim
Benefit
Number of
Policies
1
0.1
1
100
2
0.2
2
100
3
0.5
2
100
X is the variance of aggregate claims using the individual model.
Y is the variance of aggregate claims using the compound Poisson approximation,
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 Spring '11
 CharlesDann
 Probability theory, compound Poisson, individual model, compound Poisson approximation

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