Credibility And Ruin Theory Question Paper

Credibility And Ruin Theory

Course:Bachelor Of Commerce

Institution: Kenyatta University question papers

Exam Year:2008

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2008/2009
PARKLANDS CAMPUS
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE

BMS 411: CREDIBILITY AND RUIN THEORY

DATE: Friday 5th December, 2008 TIME: 2.00 p.m. – 4.00 p.m.

INSTRUCTIONS
1.
Answer question 1 and any three other Questions. Question 1 carries
30 marks.

Q1.
a)
In an investigation into the claim amounts paid under policies in a portfolio, the numbers falling in different ranges were as follows:-

Range
Numbers
Ksh.’000

0 – 500
120
501 – 1000
386
1001 – 1500
490
1501 – 2000
322
2000 - 2500
62

In order to test whether a normal distribution would provide a good model for these claim amounts, estimates of ? and ?2 were calculated from the data and the corresponding expected frequencies for each category were found to be 104, 327, 564, 309 and 76 respectively Test whether the normal distribution provides a good model for these claims. [10 marks]
b)
Explain how motor insurance claims could be represented by a poisson process. [10 marks]
c)
Explain why the probability function of the B(n.p) distribution is [10 marks]

Q2.
You have been asked to determine the expected cost and variance of claims arising from a homogenous portfolio of insured risks by building a model.
i)
State the type of model most likely to be used, giving reasons. [8 marks]
ii)
Outline the steps you would take in developing the solution. [12 marks]

Q3.
a)
The sizes of claims under a certain type of policy are distributed normally about a mean of Ksh 1.8 million and with a standard deviation of ksh 400,000. Find the probability that the sizes of two randomly selected claims differ by more than Ksh 500 000. [10 marks]
(b)
Explain what is meant by the aggregate claims process and the surplus process for a risk. [10 marks]

Q4.
Define the probability of ruin in infinite/finite and continuous/discrete time and state and explain relationships between the different probabilities of ruin. [20 marks]

Q5.
Exhaustively discuss the Bayesian approach to credibility theory and show how it is used to derive credibility premiums in simple cases. [20 marks]

Q6.
a)
List the possible sources of risk that a life insurance company might be exposed to. [12 marks]
b)
The aggregate claims process model is expressed by the equation:-
U(t) = u + ct – S(t), t 0
Explain the rationale behind the equation defining the aggregate claims
process. [8 marks]

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