Homework Assignment 24:
(1) Aggregate claims has a compound Poisson distribution with
λ
= 1 and p(1) = p(2) = 0.5.
For a premium of 4.0, an insurer will pay total claims and a dividend equal to the excess,
if any, of 75% of the premium over 100% of the claims.
Determine the expected
dividend.
(Ans 1.701)
(2)
For a certain group, aggregate claims are uniformly distributed over (0,10).
Insurer A
proposes stoploss coverage with a deductible of 6 for a premium equal to the expected stop
loss claims.
Insurer B proposes group coverage with a premium of 7 and a dividend equal to
the excess, if any, of 7
k
over claims.
Calculate
k
such that the expected cost to the group is
equal under both proposals.
(Ans 0.90)
(3) An insurer has an aggregate claims process that is compound Poisson with
λ
= 1 and p(x)
= (1/4)e
x/4
, x>0.
With no reinsurance, the insurer has a relative security loading of 1.25.
The insurer purchases reinsurance that has expected claims of 2.
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 Spring '11
 CharlesDann
 Actuarial Science, Poisson Distribution, Probability theory, Compound Poisson distribution, Financial reinsurance, relative security loading

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