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Homework Assignment 23:
(1) An insurance company sold oneyear term life insurance on a group of 2,300 independent lives as
given below:
Class
Benefit Amount
Prob of Death
Number of Policies
1
1
0.10
500
2
2
0.02
500
3
3
0.02
500
4
2
0.10
300
5
2
0.10
500
The insurance company reinsures amounts in excess of 1
on each life
.
Formulate a compound Poisson
approximation to the distribution of aggregate
reinsured
claims by matching the probability of no
claims. (Ans
λ
= 104.49112, p(1) = 0.90333, p(2) = .09667)
(2) Using the recursion formula (12.4.16) on page 385, tabulate the distribution function of the compound
Poisson approximation in problem (1) in a spreadsheet.
The reinsurer wishes to charge a premium that
is sufficient to guarantee that it will lose money 5% of the time on such groups.
Use the distribution
function to obtain the appropriate premium.
Your solution should include a spreadsheet or a few
sample calculations to document how the premium was obtained
.
(Ans: F
S
(133) = 0.94524 and
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This note was uploaded on 05/11/2011 for the course STOR 472 taught by Professor Charlesdann during the Spring '11 term at University of North Carolina School of the Arts.
 Spring '11
 CharlesDann

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