The Sad Man
09-19-2005, 12:29 AM
Here's my take on this paper. Writing these notes will help me later on and hopefully it will be of use to someone else too. I'm think I'm only going to memorize the calculation type procedures and some of the more basic facts. I agree with Purple Princess that overall it is a poorly written article, although All10's summary was lacking, e.g. how could they leave off the important formula from pp. 247-8? Anyway, I see these common techniques they continually test you on.
1. Going from Excess Paid LFD to Excess Reported LDF or vice versa. In this case, either Paid or Reported(Incurred) LDFs will be given and one must calculate the other using the relationship:
Paid LDF from i to j * (Paid/Reported at i / Paid/Reported at j) = Reported(Incurred) LDF from i to j I'd hope that the Paid/reported ratios will be given, although be careful not to use outstanding/reported instead without substracting these from 1.
2. Easy formula to remember is that from 27 months on, report year LDFs are 6 months ahead of accident year LDFS, so that Accident year @ 21 months = Reported year at 27 months. I doubt this would be tested directly but it very well might be used as an intermediate step.
3. The Pareto distribution formula (Bear Review?):
D*(X1/K1)^(Q_i-Q_j)
In this case, we want to go from an LDF, defined as D from period i to j, in a lower layer (K1 to K2) to an LDF in a higher layer (X1 to X2). The above formula accomplishes this. Note that K2 and X2 might be unbounded or infinite (which is what I commonly see on the job). They are not directly used in the formula however IF X2 and K2 are present the following relationship must hold: X2/K2 = X1/K1.
Q_i and Q_j are the estimated Pareto parameters at periods i, j. I hope they would be given if we are to be tested on this formula. If you see "Pareto" and it's a calculation problem, there's an extremely high likelihood you need to use the above formula.
4. The important formula I couldn't find listed in All10. Uses f(x) where x is the rentetion and f(x) is defined as the ratio of losses excess of x to total ground up losses. Also uses development factors for the given retentions, x's.
To calculate the LDF from retention x1 to x2:
( f(x1)-f(x2) )/( f(x1)/LDF_x1 - f(x2)/LDF_x2 )
Note this will be the LDF for whatever period the LDF is defined as, e.g. n to ult. Often you'll have to calculate a couple LDFs and take ratio to produce the desired LDF in question e.g. n to n+1 = n to ult / n+1 to ult (see q6 on 2004 exam)
now it's time to keep the midnight oil burning and move onto Siewart. I'll leave you all with a favorite quote of mine from Doctor Faustus by Christopher Marlowe. It usually helps me to keep on studying when other temptations arise in my mind.
Hell hath no limits, nor is circumscribed
In one self-place; for where we are is hell,
And where hell is, there must we ever be.
1. Going from Excess Paid LFD to Excess Reported LDF or vice versa. In this case, either Paid or Reported(Incurred) LDFs will be given and one must calculate the other using the relationship:
Paid LDF from i to j * (Paid/Reported at i / Paid/Reported at j) = Reported(Incurred) LDF from i to j I'd hope that the Paid/reported ratios will be given, although be careful not to use outstanding/reported instead without substracting these from 1.
2. Easy formula to remember is that from 27 months on, report year LDFs are 6 months ahead of accident year LDFS, so that Accident year @ 21 months = Reported year at 27 months. I doubt this would be tested directly but it very well might be used as an intermediate step.
3. The Pareto distribution formula (Bear Review?):
D*(X1/K1)^(Q_i-Q_j)
In this case, we want to go from an LDF, defined as D from period i to j, in a lower layer (K1 to K2) to an LDF in a higher layer (X1 to X2). The above formula accomplishes this. Note that K2 and X2 might be unbounded or infinite (which is what I commonly see on the job). They are not directly used in the formula however IF X2 and K2 are present the following relationship must hold: X2/K2 = X1/K1.
Q_i and Q_j are the estimated Pareto parameters at periods i, j. I hope they would be given if we are to be tested on this formula. If you see "Pareto" and it's a calculation problem, there's an extremely high likelihood you need to use the above formula.
4. The important formula I couldn't find listed in All10. Uses f(x) where x is the rentetion and f(x) is defined as the ratio of losses excess of x to total ground up losses. Also uses development factors for the given retentions, x's.
To calculate the LDF from retention x1 to x2:
( f(x1)-f(x2) )/( f(x1)/LDF_x1 - f(x2)/LDF_x2 )
Note this will be the LDF for whatever period the LDF is defined as, e.g. n to ult. Often you'll have to calculate a couple LDFs and take ratio to produce the desired LDF in question e.g. n to n+1 = n to ult / n+1 to ult (see q6 on 2004 exam)
now it's time to keep the midnight oil burning and move onto Siewart. I'll leave you all with a favorite quote of mine from Doctor Faustus by Christopher Marlowe. It usually helps me to keep on studying when other temptations arise in my mind.
Hell hath no limits, nor is circumscribed
In one self-place; for where we are is hell,
And where hell is, there must we ever be.