Life Contigencies Question Paper

Life Contigencies

Course:Bachelor Of Commerce

Institution: Kenyatta University question papers

Exam Year:2010

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
SECOND SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR
OF COMMERCE
BMS 313: LIFE CONTINGENCIES

DATE:
Wednesday 14th April 2010
TIME: 8.00a.m – 10.00am

INSTRUCTIONS
Answer QUESTION ONE and any other TWO QUESTIONS
Support your answers with relevant illustrations/examples

Q1.
a)
Describe what is meant by adverse selection in the context of a life insurance company’s underwriting process and give an example. [3marks]
b)
Describe how occupation affects morbidity and mortality. [4marks]
c)
Describe briefly the following terms: Gross premium reserves. [2marks]
d)
Using the hint that
?t ? s?q

P ? P x
P
, show that
q
x
?
for 0 ? s < ? 1

t
x
s
x
t ?s x?s
t ?s x? s
1? sqx

[5marks]

Using an assumption of a uniform distribution of deaths.
[5marks]

e)
A life insurance company has issued for a number of years whole-life regular premium policies to a group of lives through direct advertising. Assured lives are only required to complete an application form with no further evidence of health. Outline the forms of selection that the insurer should expect to find in the mortality experience of lives.
[3.3.3}

f)
Apart from age and duration, what other factors could you expect to affect observed mortality rates? Give at least three.
g)
Give a brief description in words for the following symbols.
i)
q
ii)
e
[2.2marks
m / n
x
x

Q2.
a)
For a double decrement table in which

?a??1 ? ?1000 x? 1?
?
,
?a??2 ? ,1 ?al? ?
,
000
,
1
find the express for
x
x
0

?al? and ?ad?1
x
x

b)
For a certain cohort of population, l ? 1
for ?x ? 0?
x
?1 x? 2?
?
0

Calculate

i)
the complete expectation of life,

ii)
the force of mortality at age 1 year,

iii)
the chance that a newly-born animal will die between ages 1 and 2 years.

Q3.
i)
Show that if mortality experience conforms to Gompeterz’s law, then:
? logc ?

? log?? log p ? log
? log
x ?
?
?
? B?c ? ?
x
c
1 ?

ii)
Suggest how this property could be used.

Q4.
a)
Could the value of the following using commutation columns of the

A1967-70 table at 4% interest;

i)
ä40

ii)
ä[40] iii)
10/15 ä[30]

b)
Dan aged 30 select, is used with a whole life assurance policy whose annual premium become half ten years. On the basis of the A 1967-70 tables of mortality and 4% interest, calculate the amount of this premium.

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