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ACT348F  TERM TEST 2  NOVEMBER 21, 2001
Print your name and student number clearly on each page
This is a closed book test
.
Do all work on this question paper, with work for question 1 on this page
(use both sides if necessary), work for question 2 on the next page, etc.
All calculations should be
done to
.
Answers are expected to have at least 4 digit accuracy.
at least 6 digit accuracy
1.
A fully discrete 2year endowment insurance issued at age
has a
equal
%
death benefit
to
Terminal Reserve:
.
The endowment
±²²² b
³ ~ ±²²² b = Á ³ ~ ±²²² b =
benefit paid to survivors at age
is 1000.
You are given that the annual effective
%b´
interest rate is
, and
.
µ ~ À±
¶ ~ À´ Á ¶
~ À·
%
%b
(a)
Show that the annual benefit premium for the policy is 658 .
(b)
Find
and
.
==
(c)
Formulate the unconditional 2nd year net cash loss random variable,
.
*
BONUS: Formulate
and show that the unconditional expectation
.
*
,¸* b#*Μ~²
Solution:
(a)
¨
±
¹~)
h # ¶ b
#=
O
c
~
c
b
%b
±
S º± b #» ~ ±²²²º#¶ b # ¶
» b ±²²²# S ±À¼²¼± ~ ±Á ´½¾À´² S
~ ¾½¿
±±
±
%
%b
.
Or,
and
;
¾½¿º± b #» ~ ±´½¾À´
±²²²º#¶ b # ¶
» b ±²²²# ~ ±´½¾À´
%
%b
since they are equal
658 is the benefit premium.
±
~
(b)
±
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 Fall '04
 Broverman

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