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MATH 471: Actuarial Theory I
Homework #2: Fall 2010
Assigned September 1, due September 8
1. Suppose:
s
(
x
) = exp[

x
2
2500
] for
x
≥
0.
Calculate the force of mortality at age 45.
(0.036)
2. Suppose:
μ
x
= 0.05 for 50
≤
x <
60;
μ
x
= 0.04 for 60
≤
x <
70.
Calculate:
4

14
q
50
.
(0.3783)
3. Suppose mortality follows modiﬁed de Moivre’s Law, where:
s
(
x
) =
(
ω

x
ω
)
α
for 0
≤
x
≤
ω
,
α >
0.
Show that:
μ
x
=
α
ω

x
for 0
≤
x < ω
,
α >
0.
4. You are given:
(i) The force of mortality for Enzo is
μ
E
x
=
kx
3
for
x
≥
0.
(ii) The force of mortality for Hayden is
μ
H
x
= 1.8 for
x
≥
0.
Calculate
k
so that
5
p
10
is the same for Enzo and Hayden.
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This note was uploaded on 02/02/2011 for the course MATH 471 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Staff
 Math

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