In the examiner report, the solution states that "Candidates were expected to correctly identify the underlying loss distribution given the graphed excess severities" but the solution is assuming exponential distribution applied to loss excess 1M.

Why is the underlying distribution exponential applied to loss excess 1M, not ground up loss?

Thanks!

In the chapter note, for excess claims/severity, the impact of inflation formula shows as below:

However, in the answer of 2012, Q15(a):

the increase in excess losses due to inflation is calculated as :

The last item in the first equate is missing, (1-Fx(A))/(1-Fx(A/t). Could you please explain why?

I understand for aggregate excess loss, the formula would not include the last item, because it has been offset by inflation impact of claim counts. How can I tell if the question is asking me to calculation inflation impact on excess severity or aggregate excess loss?

I dont quite get this - my understanding is claim previously above A will get the full increase by the inflation, but the lower limit A is unchanged, so the % increase in the excess layer is higher. In addition to that, there are some losses that are lower than A before inflation and now pierce limit A after inflation, further increase losses in excess layer.

How could the inflation for excess claims be lower than uniform inflation rate?

Reference: Past exam 2012 Question 22(c)

Could you please confirm the following:

1. Group - is this ground up claims or paid claims
2. F_1000(x) is confusing me, since the calculation is just doing normal F(x) while this notation seems to be referring to F_{XA}(x) in the BA wiki which doesn't make sense
3. Same for E_1000(X;x), the calculation is just calculating E(X;x), what does the notation of E_1000(X;x) mean?

Thanks!

I get the the ln(6m) comes from the attachment but then I just get lost where the 14.3634 and 0.7019 come from. I get the next part is to look up that answer from the table in part D, but obviously I am missing a step.

Part ii I think I understand that it is just finding the breakeven point of the QS. I just want to make sure I am not missing anything beyond that.

Thanks!

"The claim-size random variable X for a claim process has an exponential distribution with mean 1000. The expected number of claims for the ground-up process is 20. However, policy conditions limit claims to the layer between 1000 and 3000."

Part (a) wants us to find the mean and variance of the layer claim size.

My first issue is the statement of the question. The wording "policy conditions limit claims to the layer between 1000 and 3000" is unclear to me, and there are a few scenarios it could be:

1) Claims are reduced by 1000 (the "usual way"): so we pay 0 on claims in (0, 1000), X-1000 on claims in (1000, 4000], and 3000 on claims over 4000

2) Claims are not reduced by 1000 (how it reads to me): so we pay 0 on claims in (0, 1000), X on claims in (1000, 3000] and 3000 on claims over 3000

First all assume we're in Scenario 1: This seems like it should be a straight-forward application of formulas (5.11) and (2.2):

Then E[X; a+L] = E[x; 1000+3000] = (1/1000)*integral(x*e^(-x/1000)dx, 0 to 4000) + 4000(1-F(4000)) = 908.42 + 73.26 = 984.68

E[X;a] = E[X; 1000] = (1/1000)*integral(x*e^(-x/1000)dx, 0 to 1000) + 1000(1-F(1000)) = 264.24+367.88 = 632.12

1-F(1000) = e^(-1) = .3679

Putting it all together, (984.68 - 632.12)/(.3679) = 958.30

So now assume we're in Scenario 2, here we can't use the E[X;a]- type formulas, but I think it's still do-able. The expected claim size in 1000 to 3000 should be:

integral(x/1000*e^(-x/1000)dx, 1000 to 3000)/(F(3000)-F(1000)) = (536.61)/(.9502-.6321) = 1686.92

Then we have the portion above 3000: 3000(1-F(3000)) = 149.36

Putting these together gets 1836.28.

So neither of my answers are close to the value the book gives as 865 and I'm not sure if I'm reading the problem wrong or doing the math wrong or what.