ACTSC 232 - Spring 2010 - Assignment 2
Due: Friday, June 25 at 11:30 am
1. (a) Describe in words the insurances with the present values given.
i.
Z
1
=
b
20000
v
T
x
, T
x
≤
10
10000
v
T
x
, T
x
≥
10
ii.
Z
2
=
0
,
T
x
≤
15
10000
v
T
x
,
15
≤
T
x
≤
25
10000
v
25
,
T
x
≥
25
(b) Write down in integral form the formula for the expected value for
Z
1
and
Z
2
.
(c) Derive expressions in terms of standard actuarial functions for the expected
values in (b).
(d) Derive an expression in terms of standard actuarial functions for the covariance
of
Z
1
and
Z
2
.
2. Given
A
20
= 0
.
35,
A
40
= 0
.
55, and
A
20:
20
= 0
.
485
Calculate
(a)
A
1
20:
20
(b)
A
1
20:
20
3. You are given the following extract from a select life table:
[
x
]
l
[
x
]
l
[
x
]+1
l
[
x
]+2
l
[
x
]+3
l
x
+4
x
+ 4
[30]
100,000
99,899
99,724
99,520
99,288
34
[31]
99,802
99,689
99,502
99,283
99,033
35
[32]
99,597
99,471
99,268
99,030
98,752
36
[33]
99,365
99,225
99,007
98,747
98,435
37
[34]
99,120
98,964