ACTSCI 331 - Life Contingencies I
Exercises (Chapter 8)
year of death and the premium paid by the insured at the beginning of the year (if alive) are respectively
b
K
+1
=
1000,
K
=
0, 1, .
.., 24
500,
K
=
25, 26, .
..
and
k
=
8
<
:
3
k
=
0, 1, .
.., 14
2
,
k
= 15
, 16, .
..29
0,
k
= 30
, 31, .
..
:
Given that
k
A
40+
k
A
1
40+
k
:
25
k
j
a
40+
k
:
15
k
j
a
40+
k
:
30
k
j
0
0.202
0.114
10.005
13.414
10
0.316
0.149
4.386
10.806
20
0.458
0.112
±
6.929
40
0.744
±
±
±
,
j
L
for all possible values of
j
(b) compute
10
V
,
20
V
and
40
V
. (Answers:
4.29, 120.97, 225.55, 372)
2. A special whole life insurance is issued to
(35)
with the following embedded components:
k
+ 1
) year =
b
k
+1
= 50(
k
+ 1
),
k
= 0, 1, .
..;
Using
(1)
10
V
35
= 0.111;
(2)
(
IA
)
35
= 3.352;
(3)
A
35
= 0.142;
(4)
(
IA
)
45
= 4.191;
(5)
10
V
35:
25
j
= 0.227.
,
3. A fully discrete whole life insurance issued to
(30)
has the following characteristics :
(1)
b
k
+1
=
e
0
:
06(
k
+1)
,
k
= 0, 1, 2, .
..;
(2)
v
k
+1
=
e
&
0
:
08(
k
+1)
,
k
= 0, 1, 2, .
.. .
.