Hello there, I have quite a few questions on Chapter 15, would greatly appreciate any help!
1. From eqn 2.1, it is stated that G(1) = 1. Intuitively this is clear, but just wondering if there's a mathematical derivation to this from eqn 2.1?
2. In Section 4.2, we saw the ISO's approach to derive ILFs (pg 29) using closed claims. However, it was mentioned in pg 28 that it is not appropriate to ignore open claims. Does the ISO's approach take this into account somehow?
3. In the last paragraph of Section 5.2, the core reading says that "ILFs derived from Riebesell curves are scale invariant and do not need to be adjusted for inflation or changes in currency. (provided the attachment points remain sufficiently high for the curves to be valid).". However, I do not understand how the high attachment points relates to scale invariance?
4. Is it right to think that Riebesell curves are just specific ILFs that only consider multiples of 2 of the sum insured, while general ILFs can include any limit?
Section 6.1: Inferring treaty loss distributions from exposure rating
5. I am struggling to understand what this section is all about.
- Is the 'exposure rating' here just referring to exposure curves specifically?
- Is the section trying to start from an exposure curve obtained from a treaty without any aggregate features, infer the underlying treaty's aggregate loss distribution; then only estimate the impact of the aggregate features on the treaty and adjust the exposure curve rates from there?
6. Here, we are trying to obtain the aggregate loss distribution. Previously in pg 7, it was stated that we only look at the limited expected severity and ignore frequency as we are assuming frequency and severity to be independent.
- Is it right to say that in pg 7, we are just using the severity to obtain our loss costs at each limit, hence frequency is not required; while in Section 6.1, both frequency and severity distributions are required as we need to obtain the aggregate distribution to price in the aggregate features?
7. In pg 35, "We can use the following approach to make sure that the severity distribution chosen is consistent with the exposure rating (and hence the underlying risk profile and assumed original loss severity distributions)."
- From what I understand, we are looking at a single layer (i.e. from attachment point of the treaty to the exit point), and we want to obtain a severity distribution for this layer, making it consistent with the original loss severity distribution that was used in obtaining the layer loss cost C_L for this layer (under the assumption of no aggregate features yet). Is this correct?
- However, how does E(N)S(D), i.e. the expected frequency of a ground up loss of size D or greater, relate to obtaining a severity distribution for the layer? Shouldn't it be more related to the frequency distribution?
8. Still in pg 35, one of the process points says "We estimate the aggregate loss for each layer on the exposure rated basis."
- Does this mean obtaining the C_L loss cost for each narrow layer using the original exposure curve (found without any aggregate features yet)?
Section 6.2: Exposure adjustment in treaty experience rating
9. "We can use exposure rates..." - Is the exposure rate just referring to the rates based on exposure curves specifically?
10. The last core reading paragraph: "One way around this is to use historical limits profiles....."
- I am struggling to understand this paragraph, could you please rephrase it somehow?
Sorry for the long questions and thank you!
1. From eqn 2.1, it is stated that G(1) = 1. Intuitively this is clear, but just wondering if there's a mathematical derivation to this from eqn 2.1?
2. In Section 4.2, we saw the ISO's approach to derive ILFs (pg 29) using closed claims. However, it was mentioned in pg 28 that it is not appropriate to ignore open claims. Does the ISO's approach take this into account somehow?
3. In the last paragraph of Section 5.2, the core reading says that "ILFs derived from Riebesell curves are scale invariant and do not need to be adjusted for inflation or changes in currency. (provided the attachment points remain sufficiently high for the curves to be valid).". However, I do not understand how the high attachment points relates to scale invariance?
4. Is it right to think that Riebesell curves are just specific ILFs that only consider multiples of 2 of the sum insured, while general ILFs can include any limit?
Section 6.1: Inferring treaty loss distributions from exposure rating
5. I am struggling to understand what this section is all about.
- Is the 'exposure rating' here just referring to exposure curves specifically?
- Is the section trying to start from an exposure curve obtained from a treaty without any aggregate features, infer the underlying treaty's aggregate loss distribution; then only estimate the impact of the aggregate features on the treaty and adjust the exposure curve rates from there?
6. Here, we are trying to obtain the aggregate loss distribution. Previously in pg 7, it was stated that we only look at the limited expected severity and ignore frequency as we are assuming frequency and severity to be independent.
- Is it right to say that in pg 7, we are just using the severity to obtain our loss costs at each limit, hence frequency is not required; while in Section 6.1, both frequency and severity distributions are required as we need to obtain the aggregate distribution to price in the aggregate features?
7. In pg 35, "We can use the following approach to make sure that the severity distribution chosen is consistent with the exposure rating (and hence the underlying risk profile and assumed original loss severity distributions)."
- From what I understand, we are looking at a single layer (i.e. from attachment point of the treaty to the exit point), and we want to obtain a severity distribution for this layer, making it consistent with the original loss severity distribution that was used in obtaining the layer loss cost C_L for this layer (under the assumption of no aggregate features yet). Is this correct?
- However, how does E(N)S(D), i.e. the expected frequency of a ground up loss of size D or greater, relate to obtaining a severity distribution for the layer? Shouldn't it be more related to the frequency distribution?
8. Still in pg 35, one of the process points says "We estimate the aggregate loss for each layer on the exposure rated basis."
- Does this mean obtaining the C_L loss cost for each narrow layer using the original exposure curve (found without any aggregate features yet)?
Section 6.2: Exposure adjustment in treaty experience rating
9. "We can use exposure rates..." - Is the exposure rate just referring to the rates based on exposure curves specifically?
10. The last core reading paragraph: "One way around this is to use historical limits profiles....."
- I am struggling to understand this paragraph, could you please rephrase it somehow?
Sorry for the long questions and thank you!