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ACTSC 431  Loss Models 1
FALL 2007
TEST #2
Name :
ID Number :
1.
(12 marks)
Suppose that the per payment r.v.
Y
p
is EXP
(
= 50)
distributed. In addition, the number of
payments
N
p
±
= 3
) distribution with a probability mass at
0
,
p
M
0
, of
0
:
2
.
The actuary responsible of reviewing the previous actuary±s work decides to use a slightly di/erent model for
the next period based on the claim experience :
the per payment r.v.
Y
p
has the same distribution
the distribution of
N
p
(see above) will be used instead for the number of losses
N
L
We assume that a loss results in a (nonzero) payment with probability
0
:
9
(independently of
N
L
).
(a)
(4 marks)
Prove that the new distribution for
N
p
(
±
= 2
:
7)
with probability
mass at
0
equal to
0
:
2147
.
1
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View Full Document(b)
(4 marks)
Calculate the probability that the aggregate payment for the portfolio exceeds
100
using a
normal approximation.
(c)
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 Spring '09
 laundriualt

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