ASSIGNMENT 5 – ACTSC 431/831, FALL 2008
Due at the beginning of the class on Thursday, November 27
.
1. Assume that the aggregate losses in a portfolio are a collective risk model
S
=
∑
N
i
=1
X
i
,
where
N
has the following pf
k
0
1
2
3
4
5
Pr
{
N
=
k
}
0.1
0.2
0.2
0.2
0.2
0.1
,
and
X
1
, X
2
, ...
have the same distribution as
X
with the following pf
k
2
4
6
Pr
{
X
1
=
k
}
1/5
3/5
1/5
.
(a) Calculate the stoploss premium
E
[(
S

5)
+
].
[6 marks]
(b) Calculate the stoploss premium
E
[(
S

4
.
6)
+
].
[5 marks]
(c) Calculate
V ar
[(
S

4)
+
].
[7 marks]
2. The aggregate losses for an insurer are a collective risk model
S
=
∑
N
i
=1
X
i
, where
N
has a geometric distribution
NB
(1
,
15), and
X
1
, X
2
, ...
have the same exponential
distribution with mean 20. In an excessofloss reinsurance, a reinsurer will cover the
loss
∑
N
i
=1
(
X
i

25)
+
, and in a stoploss reinsurance, a reinsurer will cover the loss
(
S

150)
+
.
(a) Calculate the net reinsurance premium for the excessofloss reinsurance.
[4 marks]
(b) Calculate the net reinsurance premium for the stoploss reinsurance.
[6 marks]
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 Fall '09
 david
 Exponential distribution, Lundberg

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