Why are questions on ruin theory/reinsurance from the 2004-06 era so hard?

[DevonMatthews]

I find it impossible to believe that any significant percentage of students correctly answered these in the exam

 

[John Lee]

I find it impossible to believe that any significant percentage of students correctly answered these in the exam

What's causing grief Devon? Let me know and I'll see if I can help!

 

[DevonMatthews]

What's causing grief Devon? Let me know and I'll see if I can help!

Well I'm not exactly going to put my head in the oven (yet), but they seem significantly more difficult and abstract than what has been asked more recently. For example September 2005 Q1 seemed to be rather simple but the path to the solution was not at all obvious on first reading. I set the problem up correctly and was here for 20 mins trying to do double integration. I then had a quick look at the solution and when i saw the t<.... line i knew exactly what i needed to do. March 2006 Q10 (iii) seemed to again have an in-obvious route to the solution, and (iv) seemed next to impossible. The only way i was able to find a way through this algebraically was with mathematica 7.0. Also question 8 on bayesian methods from this exam was really difficult to understand. I really find it hard to believe that more than a handful of students got through that with full marks in the actual exam.

My concern is that the subject can potentially be alot harder than the more recent exams suggest..

 

[John Lee]

September 2005 Q1

You're going to hate me saying this but this is a standard ruin at first claim question. There are two cases of these - where claims are constant (A97 Q8 and S05 Q1 which is a copy!) and where claims have an exponential distribution (S99 Q5 and S07 Q5). They did a slight twist in S06 Q4 where it was discrete.

If it helps - I went through all the exam questions back to 93 when doing the CT6 flashcards and ensured there was an example on each type of exam question...

March 2006 Q10 (iii) seemed to again have an in-obvious route to the solution, and (iv) seemed next to impossible.

This should be more straight-forward now this part of the course is back in (though when it was tested this part had gone out)!

Whenever we're doing probability of ruin we start with:

P(U(t)<0)

and rearrange it to get:

P(S(t)>...)

Then since S(t) doesn't have any standard distribution we have two choices - either we use a normal approximation or we do it from first principles if the claims are something like P(X=1)=1/4 and P(X=2)=3/4.

This one we are using a normal approximation at time 1:

P(S> u + c)

But we have insruance so we now have:

P(SI > u + cnet)

Where cnet = c - creins = c - (1+q)E(SR) (which hopefully is familiar from the last part).

Hope that helps a bit...