ACT348F  TERM TEST 1  OCTOBER 11, 2000
Print your name and student number clearly on each page
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
.
at least 6 digit accuracy
Answers are expected to have at least 4 digit accuracy.
1.
A threeyear fully discrete endowment insurance with face amount $1000 is issued at age
,
B
with level annual premium of
payable at the start of each year
.
The mortality
U
for two years
probabilities are
, and the annual effective interest rate is
;& ±
; & ±
;&
B
B²
"
B²#
" ""
% $#
10%.
(a)
Write out the pointbypoint expression for the issuedate loss random variable .
P
(b)
Find the equivalence principle premium.
(c)
Suppose that
.
Find
.
U&³!
!
Z +<´Pµ
Solution:
(a)
if
P&
"[email protected]¶U&*!*·!*¶
U
O&!±; &"˛%
"!!!
@ ¶U—"²@¸&)#’·%³¶"·*!*!*
U
O&"
± ; &"˛%
"!!!
@ ¶U—"²@¸&(³"·$"¶"·*!*!*
U
O¹#
±: &"˛#
&
B
#
"l
B
$
# B
(b)
I´Pµ&´*!*·!*¶Uµ—·#³¸²´)#’·%³¶—"·*!*!*¸Uµ—·#³¸
²´(³"·$"¶—"·*!*!*¸Uµ—·³¸&)!*·³%¶"·’)")#U&!pU& %)"·$³
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 Fall '04
 Broverman
 Normal Distribution, Probability theory, Endowment policy, Equivalence Principle Premium

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