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Oct 2009 Exam Discussion

Avantgarde said:
I used the normal approximation..

Could anybody else confirm which approach is correct/appropriate..??
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I recalled that I used exponential distribution which was given in Tables. Since exponential distribution has memoryless propery it was simplified to taking the integral of exponential distribution from 0 to 30.

But i did made a mistake of specifying the prob of ruin rather than prob of not ruin
 
Avantgarde said:
I agree with evergreen.. The exam was a bit more difficult in comparison to last three sittings.. Proving the time series identity (Q1), writing the linear predictor (Q4), Calculating the mean & variance through percentile method (Q5), Proving E(1/X) (Q6), Stating in the form of credibility form (Q6), Calculating the given time series data (Q7), Proving the equilibrium states in terms of k (Q8) are the major things which made this exam more difficult in comparison to last three sessions..
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I agree with both of you. I did got stuck upon various question particularly time series questions, Q1 and Q8, and the question of credibility theory and loss distributions. The question to find the estimated parameters of lognormal distribution using method of percentiles was also tough.

I notice questions were more trickier than last few sittings and moreover were time constrainted
 
Avantgarde said:
Any idea regarding the passing mark this sitting..??
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Falak Soomro said:
I recalled that I used exponential distribution which was given in Tables. Since exponential distribution has memoryless propery it was simplified to taking the integral of exponential distribution from 0 to 30.

But i did made a mistake of specifying the prob of ruin rather than prob of not ruin
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I used normal approximation however, I would appreciate if someone from Acted comment on the right technique of solving the problem
 
What did you guys do in the last question's last part? I tried to solve the problem twice but I am not confident.
 
Garcia said:
What did you guys do in the last question's last part? I tried to solve the problem twice but I am not confident.
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I think it stated that the insurer paid the amount of each claim that followed an exponential distribution. In addition to that, 50 had to be paid for each claim above 200.
 
Garcia said:
I agree, it was somewhere around 350.
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What was the form of "k" in terms of q? Any clue on that? I think I was able to bring the policyholders' distribution in terms of k but then did something wrong with the calculation of average premium stuff. My answer was quite higher as compared to the 178 value of avg premium for low risk policyholders.

the transition matrix was like :

q 1-q 0

q 0 1-q

q2 q(1-q) 1-q
 
evergreen said:
I think it stated that the insurer paid the amount of each claim that followed an exponential distribution. In addition to that, 50 had to be paid for each claim above 200.
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The expected value was the product of lambda and expected value of Y.
Expected value of Y = Expected value of X + 50 (integral of f(x) from 200 to infinity)
 
evergreen said:
Q No 6 : Cumulative claims were given and reserve was required to be calculated by using:

(a) Chain Ladder Method (6)

(b) Bornhueter Ferguson Method (6)
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Any comments on whether to include the incurred claim values while calculating reserve?
 
evergreen said:
Q No 4 : It was a GLM question.

(a) Calulate the MLE of theta(ij) (3)

(b) Express it in terms of exponential family (2)

(c) A predictor function was given as alpha + Beta * X and it was required to recommend any other suitable function. (3)
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I got the answer to part (a) as 1/(1+y)

Could someone please confirm this..!
 
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evergreen said:
Any comments on whether to include the incurred claim values while calculating reserve?
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I seriously doubt that this question is ambiguous as the given claims were on incurred basis while the paid claims were not given on the other hand..

I just read in one of the older threads that we can write to the institute regarding these kind of ambiguities on Student Consultative Committee but that link is not working..
 
evergreen said:
Q No 8 : This was a time series question and various sample values were given.

(a) Calculate the values of a1, meu and sigma (7)

(b) Apply turning points test (3)
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Could someone please confirm if the probability was coming too high for turning point test..??
 
evergreen said:
The expected value was the product of lambda and expected value of Y.
Expected value of Y = Expected value of X + 50 (integral of f(x) from 200 to infinity)
Click to expand...

I applied the same method for E however calculating V was a bit tricky
 
LandBli said:
My matrix was the same also. I couldn't get the average premium to equal their value of 178 either - is there anyone that could?!
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I don't think we were required to confirm the value of that premium for low risk policyholders, nonetheless, it would have verified the preceding calculations. What was the expression for "k" any idea? I think it was something like :

1/(1-q+2q2-q3)
 
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