September 2007 Q1

I'm a bit confused about the wording in this question, I started answering by putting E(N) = 0.1 and E(X) = 0.5 and working out the mean and var parameters for S the aggregate distribution, so I could then work out the lamda + cr = lamda * M(r)

How come it just uses X?

When would I have to calculate the parameters for S?

Can someone help please? Thanks

 

Is there anyone who can help me with this - I know it's a bit close to the exam but I would really appreciate it! Thanks

 

You're on the right lines with your formula:
lambda + cr = lambda * M(r)

But if you also remember that c = (1+theta) * lambda * E(X)

then you'll find that the lambdas all cancel out and you're left with:

M(r) = 1 + (1+theta) * E(X) * r

(This also shows that the probability of ultimate ruin doesn't depend on lambda.)

I hope that helps a bit...

 

Thanks - I may not have worded it correctly!

I meant why don't you have to find out parameters for S as a distribution? Using E(N) and E(X) - some past exam questions need you to do this and some don't. I guess it's confusing when it says compound distribution.

 

Although you have an aggregate distribution, this question is about ruin theory, so you have identified that you need to use the formula below with the lambdas. Within this formula, the lambdas are the E(N)s and the E(X) and M(r) terms relate to the amounts. So you wouldn't have any need here for the E(S) calculation.

If you had a question that asked about the distribution of aggregate claims, or the probability that aggregate claims exceeded a specific amount then you would need to calculate E(S) and Var(S).