F 2015 13a
From the Fisher section for this chapter, ratable losses "may or may not be subject to a per-occurrence loss limit. If they are, as mentioned above, the charge for the expected losses above the per-occurrence loss limit may be included in the basic premium amount or may be kept separate from the basic premium" (p. 19). The model solution does not mention that the excess losses could be part of the basic premium. Should an assumption about this be specified in every calculation?
I'm struggling to identify all the places where an assumption can be made v. where the formula is prescriptive. What are the pieces that should always be included in the calculation of retro premium, and which pieces do we make assumptions about?
Comments
It's difficult to have a prescriptive formula for either retrospective rating or large dollar deductible policies as so much depends on the characteristics such as whether there's a per-occurrence limit/deductible, aggregate limit/deductible, min. or max. premium etc. Possibly for this reason, the Fisher text can be rather vague.
Further, the CAS can complicate things by deciding whether or not to include certain aspects within the basic premium, B.
Remember, retrospective rating pays out on all losses. The insured is charged an initial premium and then is either reimbursed or billed for additional premiums, subject to any maximum or minimum limitations.
What this means, is if there is a per-occurrence limit then we need to charge for both the losses below the per-occurrence limit as well as those above. The L part of retro prem R = (B+cL)*T takes care of the loss below the per-occurrence limit, while in this formulation, B takes care of profit, expenses, and expected loss excess of the per-occurrence limit. This can be seen in B = e - (c-1)E[A] +cI as the first two terms take care of profit and expenses, while cI takes care of the expected excess.
In general, the question should tell you if the loss limitation features such as excess of a per-occurrence limit or excess of an aggregate limit/maximum premium is incorporated in any given basic premium. In this case, the question doesn't and this is likely a reflection of the instability of the syllabus. At the time this question was written, it appears the reading always explicitly split out the per-occurrence and excess charges from the basic premium.
It's difficult to advise what's best to do other than to look at the point value and see if your solution feels like it trivializes things in which case you may need to fill in some details/state your assumptions. Further, it's helpful to think abstractly about the pieces the rating plan pays out on and make sure you've put a price to each piece. Any piece not priced is either more work to do or an assumption to possibly be stated as to where it's being accounted for.
Hope this helps.
Thank you! This helps me both from a practical standpoint of which assumptions to specify, and in understanding how the pieces of the retro rating formula connect to each other.
Hi,
As you mentioned in your response, retrospective rating pays out on all losses. The Battlewiki also states that the primary layer losses (below the per-occurrence limit) are retained by insured. I am wondering how does this work? If retrospective rating is calculating the premium on all losses, is the insurer going to pay for the primary layer losses and reimburse from the insured?
Thanks!
Hi,
In this situation it's helpful to think about how a retrospective rating plan compares to a large deductible plan and then think about the language used to describe the various pieces being priced.
A large dollar deductible plan has the insurer paying all losses and then seeking reimbursement from the insured for the deductible portion of the losses (subject to any aggregate limit). So the insured is responsible for the primary (deductible) layer. The premium charged only covers the insurer's portion of the losses, to get the true cost of covering all claims during the policy period, the insured must add on their (expected) deductible payments.
Whereas a retrospective rating plan has the insurer paying all losses and then seeking or reimbursing additional premium as needed from/to the insured. The per-occurrence limit plays the role of defining the primary layer which is the ratable loss. The basic premium charge covers losses in excess of the per-occurrence limit while the converted expected ratable loss charges for losses in the primary layer. If the actual ratable losses come in higher than expected then the insured has to pay more to the insurer, while if they come in lower than expected then the insured receives money back from the insurer. We can view this as the insured is being responsible for the primary layer, i.e. it's retaining the primary layer losses but it's paying for them in a different manner to a large deductible plan.
It's a bit like the following: Suppose expected primary losses are $2,000. You could have a large deductible plan with a $4,000 aggregate deductible and the insured would expect to pay $2,000 plus the cost of protecting against losses over $4,000. Or, the insured could have a retrospective plan with a $2,000 per-occurrence limit and maximum premium associated with an aggregate loss of $4,000. If losses come in exactly as expected then the retro plan neither owes nor receives money but the large deductible plan has to make the $2,000 deductible payment to the insurer. The total cost to the insured would be the same if we ignore differences in investment income and premium taxes.
Thanks for the explanation!
I am confused by the L = 435k/3.75 + (650k - 435k) . I feel like I am missing something really obvious.
I'm assuming you're referring to determining the cash flow for the retrospective rating plan at 18months.
Remember, a retro plan pays for all losses as follows. It charges a fixed amount for the expected excess losses (those over the chosen per-occurrence limit) and then charges a variable amount for the losses below the per-occurrence limit as they come in. This is how the insured is rewarded for good loss experience.
In the question the first row of the second table gives the expected ultimate loss when there is no per-occurrence limit and when there is a per-occurrence limit. As such, the expected ultimate excess loss is the difference between these two figures, i.e. $650,000 - $435,000 = $215,000.
To determine the retro premium charged at 18-months we need to know the ratable loss, i.e. the actual losses below the per-occurrence limit. Since we're told at the top of the question we have an incurred retro plan, we use the 18-ultimate incurred LDF to estimate the ratable loss at 18-months using the expected ultimate loss below the per-occurrence limit. This is the $435,000 / 3.75
Putting it all together, the retro premium at 18 months is the sum of
This is then all multiplied by the tax multiplier. Finally, to get the cash flow you should compare it to the premiums paid to date.
Hi
I still confused what is the difference between 2015.13.a and 2017.15.a
they both want cashflow at a given time for retro plans，2017.15 uses limited incurred loss to calculate without considering excess part
Am I missing something here？
The difference here is how the syllabus readings have changed over time. The Fisher text today says the basic premium may or may not include a charge for losses in excess of the per-occurrence limit. The text used on older exams said the basic premium does not include this charge.
So 2015 adds the charge for losses excess of the per-occurrence limit to the basic premium. Whereas 2017 assumes this charge is already embedded in the basic premium.