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Loss Models Question Paper

Loss Models

Course:Bachelor Of Commerce

Institution: Kenyatta University question papers

Exam Year:2009

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
COMMERCE

BMS 407:
LOSS MODELS

DATE: Wednesday, 23rd December, 2009
TIME: 8.00 a.m. – 10.00 a.m.
------------------------------------------------------------------------------------------------------------
INSTRUCTIONS:
Answer question ONE and any other TWO questions.

Q.1
a)
Describe the essential characteristic of liability insurance. (2 marks)

b)
Give two of the main types of liability insurance, stating for each example
a
typical
insured
peril.
(6
marks)
c)
Describe the benefits and limitations of modeling in actuarial work
(6 marks)

d)
The government of Tonga, a small country has asked you to construct a
model for forecasting future mortality.

Outline the stages you would go through in identifying an appropriate
model.

(4 marks)

e)
Write down the general statistical model for the run-off triangle claim and
explain the terms used.
f)
Give a brief definition of the following terms
i)
Estimated
ultimate
loss (2
marks)
ii)
Estimated
loss
reserve
(2
marks)
Page 1 of 3

iii)
Using the expected loss ratio method, calculate the Estimated
Ultimate loss and Estimated loss reserves using the data below.
2005 Earned premium (Kshs) = 65,000
Expected loss ratio = 60%
Losses paid to date = 15,162

(4 marks)

Q.2
The following information is available for a motor insurance portfolio:

The number of claims settled:

Development Year

Accident Year
0

1
2

2006
442
151
50

2007
623 111
2008
681
The cost of settled claims during each year (in 000’s):

Development Year

Accident Year
0

1
2

2006
6321 1901
701

2007
7012 2237
2008
7278
Claims are fully run off after year 2. Calculate the outstanding claims reserve
using the average cost per claim method with grossing up factors. Inflation can
be
ignored.
(20
marks)

Q.3
A claim size distribution is modeled using a simple distribution with density of
the form
?k 100- x .0= x=100

f (x)
(
)
=?

?
0.otherwise
i)
Verify that k = 0.0002.
ii)
Determine the mean of this claim size distribution.
iii)
Calculate the probability that an individual claim size is greater than 50.
Page 2 of 3

iv)
Calculate the probability that an individual claim size is less than 60 given
that it is greater than 50.
(20 marks)

Q.4 Suppose
X1, X2……………Xn is a random sample of claims from a normal
population with mean µ which is known and the variance 2
s which is unknown.
Determine the minimum variance unbiased estimator of 2
s . (20
marks)

Page 3 of 3

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