Thoughts on October 2015 paper?

How difficult do you feel the exam was

 

Difficulty level was above normal and the reason for that was Time Series question and theory part(*for me*)...I felt like I was writing a history paper :|..however other question were quite routine.Just hoping passing marks are somewhere between 50-55
Waiting for Sir John Lee's review of the paper.

 

tough

I thought the paper was difficult. I could not do 28 marks of the paper. It's a slim chance that I would pass.

 

Very interesting questions. I thought the monte-carlo simulation question was quite challenging. The rest(Other than the Normal-Normal proof + half of the vector time series) was okay.

 

The questions from what I remember were as follows, and have put my answers down.
Tutors, I would greatly appreciate if you could comment on the questions I have....at this rate I'm thinking at the worst, I would have scored about 57ish...Unless Question 1 is right where I'm thinking I could have scored 0! Though am expecting mid-60s...

Question 1: Find the number of simulations (3 marks)
Answer: I think I got about 958 as the answer or something in the 900s? Did anyone else get that? If so, then because it was a "calculate" question, hopefully got all the 3 marks there. I just applied the standard formula for number of simulations, substituting in all the given values such as the variance.

Question 2 (a): State 3 simplifications taken for GI contracts (3 marks)
Answer: I thought this was asking for the desirable characteristics/ statements of short-term contracts (e.g. fixed in term, assume IBNER =0 for simplicity), but checked the notes after the exam and it was the other part of the core reading on the same page! So lost all these marks I think.

Question 2 (b): State 2 examples of short-term GI contracts(1 mark)
Answer: I gave a household contents policy of a fixed term of 1 year and a 1 year travel insurance policy as an answer.

Question 3 (a): Why is this particular example a zero sum game(1 mark)
Answer: I just said the two companies were in conflict with each other and that whatever one company wins, the other one loses.

Question 3 (b): Define a randomised strategy(1 mark)
Answer: I didn't really learn this and was my last question - so I just quickly stated it's when the players do not know the choices they will make, and so a probability p is assigned to the likelihood of taking one choice and 1-p for taking the other choice....don't think I explained it right to score that mark.

Question 3 (c): Find the randomised strategy (4 marks)
Answer: I got p=0.375.....but then silly me forgot to put this back into the equation to calculate the expected payoff!! Will I get at least 2 marks?? Assuming the p=0.375 is right? Because I just forgot the final step

Question 4 (a): Use a suitable prior with binomial likelihood and calculate posterior mean under quadratic loss(2 marks)
Answer: I explained that we should use U(0,1) as a suitable prior since prob. p is equally likely to lie anywhere in the range (0,1). I then obtained a posterior, which had a beta distribution - is that right?? Then I took its mean from the Tables.

Question 4 (b): Use prior beta with binomial likelihood - calculate mode of posterior (4 marks)
Answer: Similar method to 4(a). But this time obtained beta with different parameters. Calculated the log of the likelihood. Then differentiated and set equal to 0 and solved to get mode. I forgot to check the second differential to see if maximum though!!

Question 5 (a): Normal distribution proof for posterior (5 marks)
Answer: I thought these were easy 5 marks - I guess because I learned this off as I "felt" it would turn up very soon, as rarely been examined.

Question 5 (b): State mean of posterior (1 mark)
Answer: Could do this part even if (a) wasn't done, using the tables.

Question 5 (c): Write the posterior pdf in credibility form (2 marks)
Answer: Again, hopefully everyone got this (use sample mean and prior mean)


Question 6 (a): Definition of saturated model (2 marks)
Answer: Repeat of a wordy question from a few years back. Anyone who learnt verbatim would have been very happy.

Question 6 (b): Definition of pearson, deviance residuals, explain differences between them and state when they would be identical (5 marks)
Answer: Pretty much a repeat question. I don't think they have ever asked for a definition of pearson and deviance residual - would the following suffice: "Pearson residual is (y_i - mu_i)/(sqrt (var mu_i)) where mu are mu hats, and where sqrt (var mu_i) is sqrt (var Y_i) but with Y_i replaced with the fitted values"
"Deviance residual is sign(y_i - mu_i) x d_i where mu is mu hat, and where d_i is the root of the contribution of the ith scaled deviance"
I put something like that down...but feel I lost a mark there.

Question 7 (a): EBCT Model 2 calculation for Type 3 risk (6 marks)
Answer: This is where I got worried. I got a value of Z to be slightly greater than 1 because my Var(m(theta)) ended up as a small negative!! Did I go wrong somewhere??? I hope I get 3 out of the 6 marks as I feel I made a slip....

Question 7 (b): Advantage/disadvantage of EBCT 1 and EBCT 2 (2 marks)
Answer: I think the advantage of model 2 was that it takes into account the volume of business, which varies from one year to another, and so results in more accurate results.
But I wasn't sure what advantage of Model 1 was....I just wrote that it was simple and less complex than Model 2....Did I lose one of these marks?

Question 8: BF Method and assumptions (9 marks)
Answer: This was a nice question...can't remember answer though...all I remember is once the ultimate was obtained, had to subtract the paid off. No units given in question so none in answer. Assumptions I put down were: weighted average past claims inflation will be repeated in future OR the rate of claims inflation is constant, claims from earliest AY are fully run off by end of last DY, payments from each AY will develop in the same way, and the estimated loss ratio is appropriate/correct.

Question 9(a): Derive MGF of Gamma (3 marks)
Answer: This just used standard definition of M_X(t) and then required integration and showing equivalence to MGF formula given in tables.

Question 9(b): Derive coefficient of skewness of Gamma (8 marks)
Answer: What astonished me was the number of marks here in offer...as I did it too quick with little working...so scared they could knock marks off.
I just said take C_X(t) = ln M_X(t) and then coefficient of skewness = CX'''(t)/(CX''(t)^1.5)....I calculated all the derivatives and just to confirm my differentiation was right, I checked the variance with the tables.....So I guessed then coefficient of skewness must have been obtained in the right way? Hope this was right and do not chop marks off for taking a short method.

Question 10(a): Calculate adjustment coefficient to 3dp (3 marks)
Answer: From this question is where it gets hard, the paper. I was ok with this part - I showed that 0.000655 and 0.000665 gave a change in sign from 0 and hence must be 0.00066 to nearest.

Question 10(b): Some part before this I can't remember. Then calculate Min retention for insurer (6 marks)
Answer: I got stuck here in the second part. I saw in the question there was a "per claim" comment. So I ended up with an equation with one more unknown than desired. So I set lambda = 1. Was this right? Only then do I have a chance of getting all 6 marks....otherwise who knows.

Question 10(c): Explain what would happen to minimum retention if lower reinsurance premium loading (2 marks)
Answer: I said that lower reinsurance premium loading would increase net premiums received. But then my head just got confused and guessed and wrote down that it would lead to a higher minimum retention. I don't know. Was I contradicting myself here?!

Question 11(a): Write time series in vector form, with matrices M and N (3 marks)
Answer: When I first saw this, I was so chuffed! Then realised that it wasn't the same style as in the online classroom and had an extra matrix in on the LHS of the equation! Luckily I worked this out I think

Question 11(b): Prove stationary of VAR series (8 marks)
Answer: What threw me out here was the matrix on the LHS. And the notes only dealt with one matrix I think. So I just stated to maximise any potential marks, firstly that to prove stationarity, the eigenvalues must all have modulus less than 1 and that the eigenvalues are those that satisfy the equation det (A-lambda*I) = 0, where I is the identity matrix. Does this score any marks??
What then confused me was which of the M or N matrices we had to use for matrix "A" - since the question asked for beta, I just used that one, and carried out the calculation based on that, just so the examiners could see I "understood" the method in case I end up on borderline pass/fail. Anyway, then I got to an equation where beta could only be zero so I knew what I done wasn't right! Do I score any marks for demonstrating the above?

Question 11(c): Rewrite equation in VAR format and state the VAR form (3 marks)
Answer: My brain was gone by this time. The online classroom had a little look at how to convert AR into VAR but I forgot under pressure. I just stated under pressure that it was VAR(2) I think (or VAR (3) - I just looked if it was X_t-2 or X_t-3 at the lowest and quoted that - was this right??). Hope I get a mark for stating it!

Question 12(a): Find k by solving (2 marks)
Answer: This reminded of that horrible modulus exponential distribution question a few years back on MC simulation.
Forgot what I obtained as answer...involved integrating the whole pdf and setting equal to 1....so I integrated the first expression over the range (0 to 2) and then the second expression over the range (2 to infinity), added the expressions, then set equal to 1, and then solved for k. Was this right??

Question 12(b): Inverse transform method (5 marks)
Answer: I started this and then left it, because of the fact that the distribution was split into 2 parts and knew I wasn't going to get it.

Question 12(c): Acceptance rejection method (6 marks)
Answer: So I tried to scam the marks here. I just used the set algorithm written out in the notes, f(x) and h(x) were finally given in the write notation in the paper!!! (and not the other way around as in most past papers) and then computed g(x), once I calculated C. Even if I calculated C incorrectly, hopefully I will get like 3 marks??? Because I said:
- Generate u_1 from U(0,1).
- Use u_1 to generate a random variate from the distribution with pdf h(x): then I slot in there that I set u = F(x) and solved for x (it was an easy EXP(1) distribution to invert)
- Generate u_2 from U(0,1)
- If u_2< g(x), then accept x as a value generated from distribution with pdf f(x).
Otherwise if not the case, then reject x and repeat the steps.
If this is correct, then the only marks I would lose are if I calculated C incorrectly?? Which wouldn't be more than 3 marks?

 

Any comments from acted tutors regarding difficulty

Highly appreciated

 

would you deem it a hard paper or a standard one.... sorry about repeated queries

 

Actually now thinking about it and spoken to a few people on this, I feel I could hit the 70s, so I would be shocked if I don't pass this time! And it was quite a simple paper relatively to April, in the sense that every single question was a repeat pretty much of similar application - the only difference was Question 2(i) which was a new bookwork question, Question 10 (only a little bit though, very similar to other styles),Question 11(I have seen the notes and can't believe I lost probably 2/3 marks for the last part! It's just the same idea as the first part of that question! The only hard bit is the unusual nature of the matrices, which I hadn't seen before....if it was just the 1 matrix, I would have been fine as it's covered in the online classroom), Question 12 (the only bit of confusion was the splitting of the intervals, which made things more confusing....but if you demonstrated your knowledge, I'm sure some marks could be picked up)

 

Awaiting results anxiously

I did not attempt the time series, acceptance rejection and normal derivation remaining I have done justice would be interesting to wait for the results but I found this paper challenging especially the amount of marks for derivation and theory

 

I got quite similar to you for most questions beside the last 2. For question 11, were you meant to get the matrices M and N? I managed to get something quite simple for M and N made up of B. I was able to use this part to find the values of B to make it stationary and I got a range B. For the next part where you were given a different set of equations, I was able to pull the matrix and found the values for each and got VAR(2).

I found the final question do-able because I did a course similar to CT3 recently. I found k differently to you. Because it was based off a Uniform distribution that means the values of x was bounded between 0 and 50 ie you integrate to 50 rather than infinity. I did not have time to finish the acceptance-rejection method though but I wrote down the steps of how I complete it.

Overall thoughts of the exam is that it was very challenging and difficult. The questions were interesting but it was not an easy exam. Most of the standard questions were in the paper but with many twists and conditions in it. But exam is over, hope everyone did well!

 

CT 6 Exam results

Hi,

I would like to thank Mr John Lee for being always helpful and available to help students with their queries.Also your You tube videos are very good. Passed Ct 6 and now moving on to CT 8.

Thnaks again John.