AS 5103 Study Guide - Quiz Guide: Decrement Table, Increment And Decrement Operators, Life Insurance

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Published on 23 Nov 2019
Course
Professor
TEMPLE UNIVERSITY
FOX SCHOOL OF BUSINESS
AS 3502 / AS 5103 Actuarial Modeling II
AMLCR Chapter 8 Problem Set
DR. KRUPA S. VISWANATHAN
1. The Owl Insurance Company is instituting a bonus program for its newly hired
actuaries, to increase retention. The bonus is paid when the actuary resigns from
his job and is represented by
!"#$%%%& '$($%)"
, thus a bonus increasing with
longevity.
*
= 12%. There are three causes of decrement:
cause (1): resignation
cause (2): termination
cause (3): death
+,
'
-
)
'.)
= 0.04;
+,
'
/
)'
.
) = 0.005;
+,
'
0
)
'.)
= 0.01 for t > 0
Calculate the actuarial present value of this bonus for a newly hired actuary.
2. Let the data in the Standard Service Table represent a multi-state model with the
following states:
State (0): Active employee
State (1): Withdrawal (w)
State (2): Disabled (i)
State (3): Retired (r)
State (4): Dead (d)
Calculate
1
01213-
44
5
5
5
5
6 274
4- 6 278
40 6 28/
4/
.
3. A whole life insurance of 10,000 payable at the moment of death of (x) includes a
triple-indemnity provision. This provision pays an additional death benefit during
the first 25 years if death is by accidental means.
You are given:
(i)
*
= 0.07
(ii)
+,
'
9
)
'.)
= 0.01 for t > 0
(iii)
+,
'
:
)
'.)
= 0.002 for t > 0, where
+,
'
-
)
'.)
is the force of decrement due to
death by accidental means.
Calculate the net single premium for this insurance.
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4. For a triple-decrement table, you are given:
(i) Each decrement is uniformly distributed over each year of age in its
associated single-decrement table.
(ii)
;,
<'-)
= 0.1000
(iii)
;,
<'/)
= 0.0400
(iv)
;,
<'0)
= 0.0625
Calculate 1000
;,
'-)
.
5. You have a double decrement environment and the following single decrement
rates:
x
;,
<'-)
;,
<'/)
50
0.10
0.07
51
0.12
0.10
52
0.15
0.14
0.20
0.21
You are given
=7-
'9)
= 500. Calculate
(a)
=70
'9)
(b) Using the assumption of each decrement is uniformly distributed over each year
of age in the associated single decrement table, calculate
;7-
'-)
and
>70
'/)
.
6. Frank (60)’s future lifetime is subject to two causes of failure: (1) death due to
accidental causes and (2) death due to non-accidental causes. The forces of
mortality are as follows:
1+84
'-)
'
.
)
#
?
%(%$@1111111% A . B @
%(%C$11111111. D @11111111
and
1+84
'/)
'
.
)
# %(%EF
for t > 0
Calculate
1
-41;84
'-)
.
7. Brenda (25) is interested in a continuous whole-life insurance policy with a basic
benefit of 75,000 and a double indemnity provision in case of accidental death.
Cause (1) represents accidental death and cause (2) represents death from all
other causes; the force of interest is 0%. You are given:
+,
'
-
)'
.
)
#1 -
87G"
and
+,
'
/
)'
.
)
#1 0
87G"
where 0 < t < 65
If she decides to pay for this policy with annual premiums payable continuously,
what is the annual net premium for this policy?
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8. You are given forces of failure for employees at the Owl Company:
+,
'
-
)
'.)
= 0.03,
+,
'
/
)
'.)
= 0.02,
+,
'
0
)
'.)
= 0.05 for t >0
where cause (1) is termination, cause (2) is retirement and cause (3) is death.
Owl institutes an employee benefits program in which 15,000 is paid at the time
of retirement. At an annual effective rate of interest of 4%, what is the actuarial
present value for this program for a single employee?
9. You are given a three-state model.
State 0: Healthy
State 1: Disabled
State 2: Dead
You are given the following transition intensities for all t:
(i)
1+,
4-
'
.
)
1
= 0.02;
1+,
4/
'
.
)
1
= 0.015;
1+,
-/
'
.
)
1
=0.025
(ii) All other transition intensities are equal to 0.
Jack (x), who is currently Healthy, purchases a whole life insurance that pays a
benefit of 125,000 at the moment of death regardless of which state he was in
immediately prior. You are given a force of interest of 1.5%.
Calculate the net single premium for this policy.
10. You are given the following forces of mortality for a certain population:
+,
'
-
)'
.
)
#1 /
37G"
and
+,
'
/
)'
.
)
#1 0
37G"
where 0 < t < 45
Cause (1) is death due to non-accidental means and cause (2) is death due to
accidental means.
Calculate
1
7
1;1,
'-)
.
11. Millie (65) has just began working for the TU Company which has instituted an
employee benefits plan with the following two provisions:
*A benefit of 2,000 is paid at the time of retirement if she leaves due to retirement
during the next 5 years.
*A bonus of 5,000 is paid when she completes her five-year anniversary working
for the company.
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