The graph shows two curves - one for the total loss (solid line) and the other for the limited loss (dashed line). We're told the total loss represents the aggregate losses when there is no per-accident limit.
Table M uses the aggregate loss without the application of any per-occurrence (per-accident) limit. So we need to reference the solid line, not the dashed line. Thus, at entry ratio r1, the Table M savings is A rather than A+B which is the Table L savings at r1.
Thank you! Based on your response, I have a couple follow-up questions.
For part 4), if similar logic applies to Table L, which incorporates the per-occur. (acc.) limit and aggr limited losses. Therefore, its savings is A+B. Is this correct thinking?
what about limited table M which also incorporates per-occur. limit? What's its charge and savings in term of the areas?
Thank you once again! Referring back to part (a) regarding insurance savings for Table L: the reasons A and B are subtracted from the insurance charge. Is it correct to think that:
1) For B, it overlaps with the excess loss.
2) For A, I am not so sure. Since it is between the unlimited loss and r1, does subtracting A reflect that the losses are bound by min prem?
Areas A and B both lie below the entry ratio r1. This means they are associated with losses which are smaller than the loss associated with the minimum premium. So the net insurance charge should be reduced to reflect the insured is "paying more" via the minimum premium to cover these losses.
You are also correct that area B overlaps with the charge for losses in excess of the per-occurrence limit. However, under the Table L approach we are pricing both the aggregate and per-occurrence limit simultaneously so this is less of a concern than the minimum premium consideration.
Could you help me understand Table L savings vs Limited Table M savings?
Here's my confusion: The table L charge is B + E + H + I, as it shifts from the solid line to the dotted line w/ aggregate limit. Table L does both per occurrence and aggregate loss in one go. If the question had asked for Limited Table M charge, the answer would have been just I.
This is very nuanced. We cannot readily get the Limited Table M charge and savings from these diagrams. This is because the entry ratios are different.
The Table M and Table L have entry ratios which have the expected unlimited losses in the denominator. So we can directly compare points on the graph. However, the Limited Table M has expected limited losses in the denominator. So the Limited Table M charge at entry ratio r2 (using 2013 Q15) corresponds to the entry ratio r2 * E[A]/E[A_D] which is shifted up because E[A]>=E[A_D]. Therefore, we do not have enough information to say what the Limited Table M charge and savings would be.
Comments
The graph shows two curves - one for the total loss (solid line) and the other for the limited loss (dashed line). We're told the total loss represents the aggregate losses when there is no per-accident limit.
Table M uses the aggregate loss without the application of any per-occurrence (per-accident) limit. So we need to reference the solid line, not the dashed line. Thus, at entry ratio r1, the Table M savings is A rather than A+B which is the Table L savings at r1.
Thank you! Based on your response, I have a couple follow-up questions.
Thank you once again! Referring back to part (a) regarding insurance savings for Table L: the reasons A and B are subtracted from the insurance charge. Is it correct to think that:
1) For B, it overlaps with the excess loss.
2) For A, I am not so sure. Since it is between the unlimited loss and r1, does subtracting A reflect that the losses are bound by min prem?
Areas A and B both lie below the entry ratio r1. This means they are associated with losses which are smaller than the loss associated with the minimum premium. So the net insurance charge should be reduced to reflect the insured is "paying more" via the minimum premium to cover these losses.
You are also correct that area B overlaps with the charge for losses in excess of the per-occurrence limit. However, under the Table L approach we are pricing both the aggregate and per-occurrence limit simultaneously so this is less of a concern than the minimum premium consideration.
Could you help me understand Table L savings vs Limited Table M savings?
Here's my confusion: The table L charge is B + E + H + I, as it shifts from the solid line to the dotted line w/ aggregate limit. Table L does both per occurrence and aggregate loss in one go. If the question had asked for Limited Table M charge, the answer would have been just I.
Table L savings, though, is A + B. From https://battleacts8.ca/8/wiki/index.php?title=Fisher.LimitedTableM#Limited_Table_M_&_Lee_Diagrams, isn't that the Limited Table M savings? If it's handling both the per occurrence and aggregate limit at once, why isn't it just A?
This is very nuanced. We cannot readily get the Limited Table M charge and savings from these diagrams. This is because the entry ratios are different.
The Table M and Table L have entry ratios which have the expected unlimited losses in the denominator. So we can directly compare points on the graph. However, the Limited Table M has expected limited losses in the denominator. So the Limited Table M charge at entry ratio r2 (using 2013 Q15) corresponds to the entry ratio r2 * E[A]/E[A_D] which is shifted up because E[A]>=E[A_D]. Therefore, we do not have enough information to say what the Limited Table M charge and savings would be.