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FIN 3220A Actuarial Models I
First Term 20052006
Assignment 2
Hand in the solutions on or before 31 October 2005.
1.
A 2year term insurance is issued to (30). Benefit are payable at the end of the year of death.
The death benefit for policy year
t
is
b
t
. You are given the following:
30
2
1
1
2
31
0.1,
10
,
0
,
10,
0.6,
0.
qb
b
b
b
qi
==
−
≤
≤=
=
Find the value of
b
1
which minimizes Var(
Z
).
2.
An insurance is issued to (
x
) that pays 1,000 at the end of
n
years if (
x
) is alive, and returns the
single premium
π
at the moment of death if (
x
) dies during the first
n
years. The variance of the
present value random variable at issue can be written as
()
( )
( )
( )
22
21
2
2
1
1
2 1
::
1,000
1,000
.
xn
AA
K
+π
−
−π
+
Determine
K
.
3.
A whole life insurance of 50 is issued to (
x
). The benefit is payable at the moment of death.
The p.d.f. of the future lifetime,
T
, for (
x
) is
5000
0
100
.
0o
t
h
e
r
w
i
s
e
tt
ft
≤≤
⎧
=
⎨
⎩
The force of interest is 0.10. Calculate the net single premium (i.e.
APV
).
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 Spring '05
 CSWong

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