MATH 471: Actuarial Theory I
Homework #10: Fall 2010
Assigned November 3, due November 17
1. Consider a fully continuous whole life insurance of 1000 on (x).
Assume
δ
= 0.08 and
μ
x
(
t
) = 0.04 for
t
≥
0.
(a) Find the annual benefit premium.
(40)
(b) Find the annual 20th percentile premium.
(142.22)
2. For a fully continuous 5payment 10year endowment insurance of 1000 on
(70):
(i) Mortality follows de Moivre’s Law with
ω
= 105.
(ii)
δ
= 0.1
(a) Provide the expression for the lossatissue random variable,
L
, where
¯
P
denotes each premium.
(b) Calculate the annual benefit premium.
(120.58)
3. Each of 100 independent lives, all age 35, has mortality that follows
l
x
=
100 
x
for 0
≤
x
≤
100, and
i
= 6%.
Let
L
j
denote the lossatissue random variable for life
j
, where
j
= 1, 2,
..., 100.
(a) Determine
¯
P
(
¯
A
35
), and
var
(
L
j
) (based on
¯
P
(
¯
A
35
)).
(0.0203, 0.1187)
(b) Let
S
denote the sum of all
L
j
. Using the normal approximation, deter
mine the initial fund amount,
h
, that is necessary so that the insurer is 99%
sure that
S
will not exceed
h
.
(8.01)
4. On January 1, 2010, Pat purchases a fully continuous 5payment 10year
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 Fall '08
 Staff
 Math, Actuarial Science, Endowment policy, annual beneﬁt premium

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