Practice Questions 5 – ACTSC 431/831, FALL 2011
1. The aggregate losses for an insurer is
S
, which has the following pdf
f
S
(
x
) =
(
2500
/x
5
, x
≥
5;
0
,
otherwise
.
The premium charged by the insurer is equal to (1+
θ
)
E
[
S
], which is called the expected
value principle, or equal to
E
[
S
] +
α
q
V ar
[
S
], which is called the standard deviation
principle, where
θ >
0 and
α >
0 are constants. Determine
θ
and
α
so that
Pr
{
S
≤
(1 +
θ
)
E
[
S
]
}
= Pr
±
S
≤
E
[
S
] +
α
q
V ar
(
S
)
²
= 0
.
95
.
2. The aggregate claims of an insurer is the collective risk model
S
=
∑
N
i
=1
X
i
. You are
given:
(a) The number of claims,
N
, has a negative binomial distribution
NB
(2
,
1
/
5).
(b) The claim sizes
X
1
,X
2
,...
have the same distributions as that of
X
with the
following probability function
k
3
4
5
Pr
{
X
=
k
}
1/3
1/3
1/3
.
(c) The premium charged by the insurer is equal to the mean of aggregate claims
plus the variance of the aggregate claims.
Calculate the probability that aggregate claims will not be greater than the premium.
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 Fall '09
 laundriualt
 Variance, Probability theory, collective risk model, aggregate losses, net reinsurance premium, stoploss premium

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