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This is an older question which, while still relevant today, contains terms that previously may have been discussed in greater detail. Today, the CAS would expect you to infer what these mean.
A brief discussion of retrospective development…
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It's asking you to think about Couret & Venter's multi-dimensional credibility technique in the context of ASOP 12. How does the technique compare against using the standard approach (which is grouping workers' compensation classes into hazar…
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Update 9/1: Cleaning up this answer to keep everything in one place.
The Fisher text says (top p.90) "All other things being equal, the higher the expected number of claims, the lower the variance on the distribution of entry ratios, and t…
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Page 84 of the Fisher text outlines how the ICRLL procedure can be thought of in two ways:
- Adjusting a Table M to approximate a Limited Table M, or
- Describing how to map a Limited Table M down to a Table M.
That is,…
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The examiner's report is mathematically inconsistent in sample 2 because it plays loose with the notation in the limits. The same is true of the Fisher text on page 52.
Remember, dF(x) means a small change in F(x) and F(x) is only defined …
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The entry ratio rG is the actual loss associated with the maximum premium divided by the expected loss. We do not directly know the numerator so cannot calculate as you suggest.
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The key point here is when you switch the horizontal axis from being the cumulative claim count to the cumulative distribution (cumulative claim count percentage), you go from the total dollars paid out across all policies to the average dollars …
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Thanks for calling this out. It's a typo, f(r)dr should be f(y)dy. We've updated the wiki to fix this.
Note that dF(y) is equivalent to f(y) dy.
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This is really a question of semantics. When the horizontal axis is the cumulative claim count the shaded area is the insurer's payout across all claims. When there is no limit or deductible this is the total expected loss which you could say is …
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Yes, the net premium should cover losses in excess of the per-occurrence limit as well as those excess of any applicable aggregate limit.
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The basic premium, B, consists of a fixed expense component and the converted net insurance charge. The assumption is changing the maximum ratable loss amount doesn't alter the fixed expense component and so if B increases then the converted net …
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You don't know which pair is correct until you calculate the resulting CoV for each. The question tells us to assume the coefficient of variation is less than 100%, so we select the pair which satisfies this condition.
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Hi,
Yes, you definitely need to be able to calculate the Pareto parameters in this type of problem.
The issue you're having is with the line of best fit. In your calculation you are assuming the line of best fit goes through the poin…
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We're told the low severity loss is $500,000 and in part a we worked out the appropriate deductible is $750,000. The Lee diagram shows the deductible losses as the retained loss (light grey area). For the 2.5 million loss we're told it consists s…
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We're told the correct distribution for losses is uniform on [$0, $90,000] so E is $45,000.
Since we're told to keep the same minimum and maximum premium we need to find r_H and r_G, the entry ratios associated with the minimum and maximum …
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You raise a good point. We looked back through the Fisher text and they don't define "net deductible premium" anywhere but do mention it in their solution to Step5.
In our opinion, it's a terminology thing. B+cL is the premium before taxes…
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The data we are given is grouped so all we know is losses above 1M follow an exponential distribution based on our calculations for e(x). The memoryless property of the exponential distribution allows us to extrapolate e(x) for values of x larger…
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Your calculations are correct. The statement you're testing only holds in general according to Bahnemann. Bahnemann is implicitly making this statement in the context of claim severity distributions which are usually heavily right skewed.
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Hi,
- The source text is ambiguous about this but since layers of coverage are discussed later in the chapter/wiki, ground up claims is a reasonable assumption. You can perform the process in either context; how you interpret the results…
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In both the insurance charge example and the insurance savings example we are looking at the entry ratios, A/E, where A is the actual loss and E is the expected loss. For ease of notation we let Y = A/E.
The formulas for calculating the res…
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Thanks, good call out. 100/80 means a 0% fixed expense and 20% variable expense for an expense ratio of 20%. This is equivalent to saying the expense multiplier is 1.25 or the expense load is 25%. We've updated t…
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In part a you generate an AEP curve for the given data. In part b, we want to simulate the total insured loss (the aggregate loss) by looking at the 86th percentile of the AEP curve.
Since the AEP curve was generated using three discrete l…
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Done. It's worth noting though that aliasing is still on the syllabus. The terminology and level of detail you're expected to understand has changed. I encourage you to at least read/familiarize yourself with these battlecards in case the CAS add…
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I think this is a case of mixing perspectives as "insured" has different meanings depending on where it is used in the question. In the context of reinsurance, "the insured" means the insurer, not the insurer's policyholders.
We have an ins…
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Great question - it's one of those things that's rarely explicitly talked about in any text.
Let's suppose you're doing a territory relativity analysis. You go ahead and calculate the (credibility weighted) indicated relativities and make s…
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We looked this morning and it appears the CAS has taken all of the study kits (not just exam 8) off of their online store already :(
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This is a bit hard to advise on. According to the source texts, the State/Hazard Group Relativity is only mentioned in the Fisher reading in the context of the ICRLL adjustment. So in theory, yes, just in the context of the ICRLL adjustment.
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This is a terminology thing I'm afraid you have to get used to and also hope the CAS uses it in the right context. k is the loss elimination ratio which is a ratio to losses, whereas the excess loss factor is a ratio to standard premium.
S…
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Yes, that's correct. We'll add a clarification to the wiki shortly.
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Thanks, you're correct about the typo in #2, we've fixed the solution to use ln(25) instead of ln(75). You have the correct probability.
For #8a, the intent here is today the actuary has estimated that two years in the future t…