Fall 2002 - Course 3 Solutions

Question #34
Answer: A
b g b g = + =
µ τ x t
0100 . 0004 . 0104 .
t
p
b g =
-0.
104
τ
x
e
t
Actuarial present value (APV) = APV for cause 1 + APV for cause 2.
z5
0
z
−0. 04 t −0 . 104 t 5
−0. 04 t −0.
104 t
0
z5
−0.
144t
. , .
0
b g b g
2000 e e 0100 . dt + 500, 000 e e 0400 . dt
c b g b gh e dt
= 2000 010 + 500 000 0 004
e
b gj
2200 −
= − =
0 144 1 0.
144 5
e
.
7841
Question #35
Answer: A
R = 1 − p = q
x
x
S = 1− p × e since e
0
= e
x
b g
z
1
1
1
−k − µ x + − µ x −
0
0
So S = 0. 75R ⇒ 1− p × e = 0.
75q
x
e
e
−k
k
−k
t k dt t dt k dt
= e
−
z
z
d b g i b g
x
q
= 1−
0.
75
p
x
x
1
0
µ
x
b g
t dt
px
1−
qx
= =
1 − 0. 75q
1−
0.
75q
L
NM
1−qx
k = ln
1−0.
75q
x
x
O
QP
x
e
z
−z
1
0
k dt