Ruin - Sept 07 Q5 part (ii)

Hi, I'm confused on this question as I tried to do it by having T as the waiting time until the first claim which is exponentially distributed with parameter lambda. The solution doesn't take this approach at all, so I don't know whether it is possible to do it this way (and I have made a mistake somewhere) or it is not possible. If it is not possible, I would like to understand why.
I cannot see why this method works on September 2005 question 1, but not here, as far as I can tell the questions are asking for the same thing (though I realise you have already calculated something to help you in part (i) of s07)

Thanks for your help,
Leila

 

Sept 07 uses the more general way of solving ruin theory questions

Prob(ruin on first claim) = integral over all t {P(ruin given claim is at time t) times density function of t}dt

Sept 05 could have been done this way as well, but in that question the claims were constant values. The above way would be possible, but there is a short cut in that here the probabilty of ruin simply depends on when you get a claim.
If you were sure to get a claim of 100, you would have ruin only if you didnt accumulate 100 by the time you had a claim.
For the time, you can use the waiting time.

In Sept 07 the key difference is that the SIZE of the claim is in itself a random variable.
You could avoid ruin by a small claim, even if it is early.
Or a late, very large claim could cause ruin.
So it is not as straightforward as using waiting time only. The more general approach is needed.

 

Thanks Didster - that's really helpful (and a very speedy too!).

 

Question on T

Dear Tutor,

I have three questions re ruin theory.

1) It seems there have been a number of question on calculating probability of ruin on first claim, yet there is no mention of it either in the Core Reading or the Course Notes. Is it possible to include the material for future students?

2) Though I can apply the method underlined below, I have not understood the rationale behind it, especially the explanation given in the solutions for Q2.30 in the Q&A Bank. Appreciate it if someone can point me in the right directions.

3) If a ruin probabilities qn does not refer to using normal approx, do we still gain credit for applying the approximation? Is there a general rule for calculating ruin prob. w/o using normal approx.?

Thanks in advance.