ACT348F  TERM TEST 1  OCTOBER 17, 2001
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.
THIS IS A CLOSED BOOK TEST  NO BOOKS OR NOTES ARE ALLOWED.
A calculator may be used
1.
(a)
Express
in each of the following forms:
!
%¢ O
=²(
³
c c
(i) prospective, (ii) retrospective, (iii) premium difference, (iv) paidup insurance
(v) annuityonly, (vi) insurance only, (vii) premium only
(b)
Formulate the prospective and retrospective form of the reserve
!
%¢ O
=
.
Starting with one of these formulations, show that if
,
!±
then
!
%¢ O
7c
7
7
=~
%¢ O
c
%¢! O
c
%¢! O
c
.
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View Full Document2.(a)
With
and assuming DeMoivre's Law with
(
)
± ~ À²
~ ²³³
´ ~
!%
c%c!
c%
find
.
=µ( ¶
c c
(b)
With
(force of interest) and assuming
for all
(constant force of
±²
~À²
µ&¶~À³·
&
mortality at all ages), find
.
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 Fall '04
 Broverman
 Actuarial Science, A Closed Book, Gilbert Adair, ¢1BO

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