Hi! I was wondering if anyone could tell me why Q3 (April 2007) does not contain the conditional expectation that P(X > 100)? i.e. "the mean amount paid by the insurer on claims in which it is involved". If you compare this question with Q4 (April 2002), they both are on excess of loss with a policyholder deductible. Many thanks!!
Q3 A2007 Hi Amelia, This is a very important point you have raised and I agree that it is completely unclear how to proceed here given the ambiguity of solutions to the same question in the past papers. If the question says "claims in which the reinsurer is involved" then there is no argument, we divide by P[X>M]. If there is a possible ambiguity then you should state your assumptions and carry on. You can easily give two answers on this one, being very precise : "I am worried that the question is ambiguous. The expected claims paid by the reinsurer ON ALL CLAIMS is £a Therefore, the expected claims paid by the reinsurer ON CLAIMS IN WHICH IT IS INVOLVED is £a / P[X>M] = £b" This should surely get full marks, whatever the examiners' interpretaion of their own question? The only thing you may have done is waste time calculating the denominator P[X>M]. However, this is an issue in many exams, especially "Show that" questions - how much working should I show? do I need to go into this much detail? If in doubt leave space for the detail that may be superfluous to requirements and then come back later and fill it in! Good luck! John
Thanks John! I kept thinking I was missing something when doing the questions. Will remember to state all my assumptions in the exam
I sent a letter to the examiners about this 21 September 2007, but we have still not had a reply. So feel free to contact the big cheese directly at: trevor.watkins@actuaries.org.uk As this really needs to be sorted!
Hi John, Under the syllabus this year, the deductible payout system is actually called "Policy excess" right? They should have given us the formula for the expected payout just as they have demonstrated for "Excess of loss reinsurance" !! Thanks
Any chance a tutor could provide an update on this? Last time I received an FA and do not want to lose a mark as easy as this- since I am always under time pressure in the exam and never finish an exam, I do not want to write extra if it is not required. For a standard distribution in the tables, could I write "assume insurer is not aware of claims below deductible" and then divide by P(X>deductible) and just end it there? But for a non-standard distribution, could I write "assume insurer is aware of claims below deductible" and leave it there? Because integrating could take too long!
What do you mean by non-standard? The standard distributions that come up again and again are the uniform, exponential, pareto and lognormal - thought they have asked the normal twice (but the formula is on page 18 along with the lognormal).
Oh yes! I originally thought they could give a pdf that wasn't in the tables (i.e. non-standard) and so in that case, I would have to work from first principles - and since working from first principles takes longer, I thought I could use the reasoning as per below. Though having looked at recent papers, it has been clearer I think on what they wanted, e.g. stating clearly to calculate the prob. of reinsurer being involved
