ch11 doubts

keshav1996keshav1996
in F-11-FreqSev
  1. If we have trended frequency and severity both, then, to calculate the ultimate for a particular AY, should we use original exposure of that particular AY OR trended average exposure (from prior years including current AY) for multiplying it by (freq x sev)?
  2. In several exam problems it's mentioned as an advantage of F-S technique that it only uses paid data. So case reserve changes don't cause a problem. But, isn't it an advantage only in context of Disposal Rate technique and not FS method in general, because method 1 under FS can use reported counts and severity as well to calculate ultimate?
  3. Which problems are Alice's comments under disposal rate method referring to? Her comments discuss things to take care in problems 1-4 but those problems are nowhere to be found in the article.
  4. If an exam question says 'a ONE TIME change', then does it mean a change that will continue from that point of time in future or is it synonymous to 'a ONE-OFF change' (like increasing reserves by a huge amount only in one particular year and then normal again from next year).
  5. There was a question on estimating tail severity (Spring 2019 (Q20)) in the BattleQuiz of FS chapter. It was quite confusing and I didn't understand it from the examiner's report too. It's is not in wiki article also. Please cover this topic too along with the question's explanation.

Additionally,

  • Incremental development technique hasn't been covered anywhere yet. Neither explanation nor examples, but there are many exam questions that require usage of additive CL instead of multiplicative. Please add a section with examples and questions probably in the development technique chapter.

Thanks

Keshav

Comments

  • GrahamGraham
    edited January 2021

    I will look at your questions over the next few days and get back to you.

    Note: I don't think the additive CL method is discussed in the source text in chapter 7. It's covered in chapter 16 in the context of ALAE. Exam problems sometimes cover material from more than 1 chapter so it's possible that there are additive CL problems listed in the chapter 7 BattleTable. I will make a note of this in the wiki and provide a link to where the additive CL method is discussed chapter 16.

  • GrahamGraham
    edited January 2021

    Update for your questions 1,2:

    Question 1: I believe exam problem 2017.Fall Q20 on frequency-severity method #2 is an example of what you're asking about. You can see my solution here:

    This problem asks you to calculate the ultimate for AY 2025, which is the most recent year so the trended exposure equals the un-trended exposure anyway.

    If the problem had asked for a prior year and you had used trended frequency and trended severity, then it makes sense to use trended exposures as well. In general, everything should be on the same level.

    Question 2: You're basically right in what you're saying. The source text is a little fuzzy on this. I'm not sure which exam problems you're referring to but I think what they mean is that frequency-severity methods can be performed using only paid data. Of course, you can say the same thing about other methods as well. The way I would think about it is that if a method uses only paid data then an advantage is that it isn't affect by changes in case strength. Conversely, if a method used only reported data then an advantage is that it isn't affected by changes in settlement rate.

  • GrahamGraham
    edited January 2021

    Update for questions 3,4,5:

    Question 3: This text was leftover from a beta-version of the wiki and has now been deleted.

    Question 4: The interpretation of the term "one-time change" depends on context. Normally only 1 interpretation makes sense for the given situation.

    Question 5: (2019.Spring #20): To calculate the trended tail severity for 84 months and older at 2018 costs levels, here are the steps:

    • For an 84-month tail factor, we'll use only the 3 values in the upper right corner of the count and loss triangles. These are the values aged 84 and 96 months.
    • The basic formula for severity is losses/counts and the simple but incorrect way to compute tail severity at 84 months is (6100+2400+3900)/(81+13+61) = 80. It's wrong because the losses in the numerator require 2 adjustments: trend and legislative change.
    • Note that the legislative adjustment only needs to be applied to the 2011 values to bring them in line with cost levels in effect after Jan 1, 2012. The adjustment is a factor of 0.8. In other words, we adjust 2011 claim costs down 20% to be in line with cost levels after Jan 1, 2012. So the 0.8 factor is applied to losses for 2011 @ 84 months and 96 months which are 6100 and 2400. Keep this in mind.
    • We must also apply the severity trend to both of these 2011 losses. The trend is 6% and to bring 2011 to 2018, we apply another factor of 1.06^7.
    • Putting these 2 adjustments together for the 2011 losses at 84 and 96 months gives you the first term in the numerator of sample answer 1 in the examiner's report:
      • (6100+2400)*(1.06^7)*0.8
    • The second term in the numerator in sample answer 1 is the adjusted loss for 2012 at 84 months. Here we only need to apply the severity trend. To bring 2012 to 2018, the trend factor is 1.06^6:
      • 3900*(1.06^6)
    • No adjustments need to be made to the counts in the denominator of the severity formula so the final result is:
      • [(6100+2400)*(1.06^7)*0.8 + 3900*(1.06^6)] / (81+61+13)
      • = 101.66
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