Fisher.LimitedTableM
Reading: Fisher, G. et al, "Individual Risk Study Note," CAS Study Note, Version 3, October 2019. Chapter 3. Section 4
Synopsis: This is a quick read but you must pay close attention to how the losses are limited due to the interaction between a per-occurrence deductible and an aggregate deductible limit.
Study Tips
...your insights... To follow...
Estimated study time: 2 hours (not including subsequent review time)
BattleTable
Based on past exams, the main things you need to know (in rough order of importance) are:
- fact A...
- fact B...
reference part (a) part (b) part (c) part (d) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1)
In Plain English!
In Fisher.TableM we learned how to create a Table M to estimate aggregate loss costs without a per-claim limit. However, in reality most policies have a per-occurrence limit (or deductible) and and aggregate limit which caps the insured's maximum out of pocket. For instance, a policy may have a per-occurrence limit of $100,000 which means the insured is responsible for the first $100,000 of any claim. The same policy may also have an aggregate limit of $250,000. This means once the insured has been responsible for claims where the portion under $100,000 totals at least $250,000 then they are only responsible for $250,000 so the insured is no longer responsible for paying any part of claims.
The per-occurrence limit reduces the variance of the aggregate loss distribution by reducing the variance of the severity distribution.
There are two possible approaches for pricing such a policy.
- Separately price losses in excess of the per-occurrence limit (deductible), D, and then price for losses in excess of the aggregate limit.
- This is the Limited Table M approach that we'll discuss here.
- Price it all at once - this is the California Table L approach (see Fisher.TableL)
Question: What are two reasons it may be preferable to price separately using approach 1?
- Solution:
- There may be enough data to update the per-occurrence excess charge most often than the aggregate excess charge.
- It may be possible to use two different data sources for the calculations. This is the approach used by the NCCI.
Key Issue: Consider a policy with a per-occurrence limit of $100,000 and an aggregate limit of $250,000. Suppose a claim has come in for $275,000. This claim is $175,000 over the per-occurrence limit, but also $25,000 over the aggregate limit without even taking into account if there are any prior claims. How much of the loss is applied to each limit?
In this situation it is usual to apply the per-occurrence limit first, so $175,000 is excess of the per-occurrence limit. We count the difference, namely $100,000, towards the aggregate limit. This avoids double counting of losses.
For the remainder of this article, assume the per-occurrence excess charge is known and was calculated using losses that were not subject to an aggregate limit. Then before pricing the aggregate limit, it is important to restrict all losses by the per-occurrence limit.
Question: A policy has a $100,000 per-occurrence limit and an aggregate limit of $250,000. It experiences the following unlimited claims: $60,000; $70,000; $90,000; $110,000; $120,000.
What are the claim amounts that should be used for pricing the aggregate limit?
- Solution:
Claim Number Unlimited Amount Restricted by per-occurrence limit 1 $60,000 $60,000 2 $70,000 $70,000 3 $90,000 $90,000 4 $110,000 $100,000 5 $120,000 $100,000 Total $450,000 $420,000
- When pricing the excess charge for the aggregate limit you must use the limited amounts in the "restricted by per-occurrence limit" column.