actuarial ct6 statistical methods sample paper 2011

8/3/2019 Actuarial CT6 Statistical Methods Sample Paper 2011

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ActuarialAnswersSample Paper

CT6 Statistical Methods

We are a team of actuaries engaged for the last 3 years in assisting students specializing

in Actuarial Science. Our core team members include University toppers from leading

Commerce colleges, including SRCC, Jesus & Mary and from the Indian Institute of

Management and bring diverse work experience from Deloitte, Mercer and Milliman.

We have also worked with various MBA institutes enabling them to prepare actuarial

students professionally. Besides, we have also tie-ups with actuarial firms through which

we will help students gain live project knowledge. We are also soon starting with some

unique programs to help students in understanding the practical application of actuarial

concepts.


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ActuarialAnswersSample Paper CT6 Statistical Methods

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Our Analysis

After analyzing the IAI CT6 examinations of last 7 years, we have identified some trends, in

terms of weightage of each chapter in the examinations, which could help candidates in

preparing for this exam in a better manner.

As the result of CT6 exam in the last attempt is 0.64%, we believe there is a need to identify themore important sections where paying more attention from students can help them in cracking

the exam. Below graphs indicate the chapter wise-weightage for CT6 papers historically:

Keeping this in mind, we have developed this paper from the most appearing chapters, i.e. 1

(Decision Theory), 2(Bayesian statistics), 4 (Reinsurance), 10 (Run-off triangles), 11 (Generalized

linear models), 12 and 13 (Times series), and 14 (Monte Carlo Simulation). These havecontributed 77% of the exam for the last 7 years. This will help you do targeted revision for the

upcoming examinations. Its recommended though that you do revise for other chapters also,

but focusing on this paper will help you get the maximum ROI on your effort

Please note: The material of the sample papers are the collection of the questions from the

IAI/IOA exams based on our analysis. Actuarial Answers is not declaring/saying anywhere that

this is the product created by Actuarial Answers. There is every possibility that students will

find the questions of this sample paper in past year IAI/IOA exams

0.00%

2.50%5.00%7.50%

10.00%12.50%15.00%17.50%20.00%22.50%25.00%27.50%30.00%

1 2 3 4 5 6 7 8 9 10 11 12 &

13

14

Examw

eightage

Chapters

May2011

May2010

Nov2010

May2009

Nov2009

May2008

Nov2008

May2007

Nov2007

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

1 2 3 4 5 6 7 8 9 10 11 12

&

13

14

Exam

weightage

Chapters

Last 5 years IAI exams

Last 6 years IAI exams


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SAMPLE PAPER I

Max. Marks: 100

Time Allotted: 3 hours

Note: Use of Scientific Calculators & Actuarial Tables is allowedQ.1 A casino operator moving into a country for the first time must apply to thecasino regulator for a license. There are three types of license to choose from slots,

dice and cards each with different running costs. The casino operator has to pay a

fixed amount annually (1,300,000) to the regulator, plus a variable annual license cost.

The variable license cost and expected revenue per customer for each type of game are

as follows:

The casino operator is uncertain about the number of customers and decides to prepare

a profit forecast based on cautious, best estimate and optimistic numbers of customers.

The figures are 14,000; 20,000 and 23,000 respectively.

i. Determine the annual profits under each possible combination.[2]

ii. Determine the minimax solution for optimising the profits.[3]

iii. Determine the Bayes criterion solution based on the annual profit given theprobability distribution P(cautious) = 0.2, P(best estimate) = 0.7 and

P(optimistic) = 0.1.

[3]

[8]


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Q.2


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Q.3

where < 1 and the etform a white noise process

[3]

Q.4 Write down the general statistical model for the run-off triangle claim data andexplain the terms used.

[5]

Q.5


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[9]

Q.6 It is presumed that during the initial years of a company, the events of postingnet annual profit in successive years occur independently with probabilityp. A watchdog

agency gives a profitability score (X) to start-up companies, and keeps a record of the

number of years (Y) taken by the company to post net annual profit for the first time(Y=1,2,3,). An analyst wishes to fit a Generalized Linear Model to the paired data (X,Y)

for several start-up companies.

i. What is the distribution ofY?[1]

ii. Calculate the mean ofY.[1]

iii. Show that the distribution ofYbelongs to an exponential family, and identifythe natural parameter, the mean and the variance function.

[4]

iv.

Using the canonical link function, state a model that relatesXto the mean ofY.[3]

v. The analyst intends to fit the above model to the data (X1,Y1),,(Xn,Yn), for nstart-up companies. Write down the likelihood function explicitly in terms of the

model parameters and the data

[3]

[12]

Q.7 Consider the following probability mass function of a discrete random variableX.Px(X= 2) = 0.15

Px(X= 3) = 0.20

Px(X= 5) = 0.25

Px(X= 7) = 0.20

Px(X= 11) = 0.20


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Using the following pseudo-random numbers from the Uniform (0,1) distribution,

generate nine samples from Px: 0.011, 0.757, 0.438, 0.258, 0.981, 0.518, 0.400, 0.351,

0.672.

[4]

Q.8i. Define a Markov Process.

[2]

ii. For what value of p an AR(p) process is a (one-step) Markov Process?[1]

iii. Rearrange terms of the AR(2) process Xt = 0.5 Xt-1 + Xt-2 + et such that theresultant vector AR process becomes a (one-step) Markov Process.

(2)

[5]Q.9

Q.10

[8]


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Q.11

Q.12

Q.13 A sequence of pseudo-random numbers from a uniform distribution over theinterval [0, 1] has been generated by a computer.

i. Explain the advantage of using pseudo-random numbers rather than generatinga new set of random numbers each time.

[2]

ii. Use examples to explain how a sequence of pseudo-random numbers can beused to simulate observations from:

(a) a continuous distribution

(b) a discrete distribution

[4]

[6]

Q.14


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Q.15 Let X denote the claim amount under an insurance policy, and suppose that Xhas a probability density fX(x) for x > 0. The insurer has an individual excess of lossreinsurance arrangement with a retention of M. Let Y be the amount paid by the

insurer net of reinsurance. Express Y in terms of X and hence derive an expression for

the probability density function of Y in terms of fX(x).

[2]


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Evaluation

We would be sending out the evaluation for this exam in a weeks time. In the meanwhile,

we are open to providing one-to-one evaluation for your attempt at this sample paper. You

may email us your solutions in a document or scanned copies at

[email protected].

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actuarial ct6 statistical methods sample paper 2011

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