ch7 doubts

keshav1996keshav1996
in F-07-Development
  1. How to extrapolate tail factor by fitting exponential curve on existing LDFs? Please give a small worked example in Excel. I couldn't work it out by myself.
  2. What exactly is the estimation error mentioned in Wiki article? (I have heard it only in the context of Reserve Risk). Also, how does applying a highly leveraged CDF (say 10.0) to a loss magnifies the estimation error and that too by the same factor i.e 10.0 (also stated in Wiki article only).
  3. Should the relative proportions of premiums & losses (I suppose that's loss ratios only) for LOB 1 versus LOB 2 in the Changes in Product Mix scenario remain same over time, between LOBs or both for combining their data? According to me, for combining purposes, the growth should be consistent across LOBs only. Over time, the growth rate for an LOB may fluctuate, but as long as the fluctuation is same between LOBs, we can go ahead with combining, given other conditions are met. Please correct/add to my statement above.
  4. Pop Quiz B says that as long as development pattern b/w 2 LOBs is stable and same (or I think similar would also work), we can combine the data for reserving analysis, irrespective of whether their growth rates are same or not. Why does this result hold?

Thanks

Keshav

Comments

  • GrahamGraham

    Hi Keshav,

    1. I added a exponential regression starting at line 47 of the Excel file in the section at the link below. You might need to google "LOGEST" Excel function. It is an array function. You wouldn't be asked to do this on the exam although you might be asked about the concept. Here's the link: https://www.battleacts5.ca/wiki5/Friedland07.Development#Development_Method_-_Tail_Factors
    2. If the loss reserves for a claim are not accurate at a specific maturity then there is "case reserve estimation error". Suppose the estimation error is $1,000. If you apply an CDF of 10.0 then the error in your estimate of ultimate will be off by $10,000. But if you apply an CDF of 1.5, your estimate of ultimate is only off by $1,500. Long-tailed lines generally have higher CDFs at early maturities which is the same thing as saying the CDFs are highly leveraged.
    3. I believe your statement is correct: As long as the losses for LOB1 and LOB2 grow or shrink together then it should be ok to combine them. (In general if LOB1 and LOB2 have different development patterns and the losses for LOB2 are growing relative to LOB1 then the LDFs for the combined triangle will move closer and closer to the values for LOB2 alone. You would find it difficult to select LDFs appropriately for the combined triangle as is demonstrated in the video and in the Excel file.)
    4. It's fine to say "similar" instead of "same". Reserving is all about estimation and judgment so you would never actually have 2 LOBs where the development patterns were literally the same. About the second part of your question: When data is combined, the LDFs for the combined data is essentially an average of the LDFs for LOB1 and LOB2. If LOB2 is growing relative to LOB1 then the average LDF will move closer to the LDFs for LOB1 and will no longer be appropriate for the LOB1 subset. But if the LDFs are the same/similar, then the average LDFs will be the same as the LDFs to LOB1 and LOB2 individually so there is no problem. It's like if you take the average of 1.5 and 1.5 ==> the average still equals 1.5. The combined triangle should have a stable LDF pattern so you would be able to make appropriate LDF selections.

    I hope this answers your questions.

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