01_clark Flashcards
Describe two types of proportional treaties.
- Quota Share – the reinsurer receives a flat percentage of the premium and assumes that same flat percentage of the losses. The reinsurer pays the cedant a ceding commission which reflects differences in incurred underwriting expenses
- Surplus Share – the reinsurer assumes a part of the risk in proportion to the amount that the insured value exceeds the retained line, up to a given limit. The given limit is expressed as a multiple of the retained line
Identify the steps for pricing proportional treaties.
- Compile the historical experience on the treaty
- Exclude catastrophe and shock losses
- Adjust experience to ultimate level and project to future period
- Select the expected non-catastrophe loss ratio for the treaty
- Load the expected non-catastrophe loss ratio for catastrophes
- Estimate the combined ratio given the ceding commission and other expenses
Briefly describe a sliding scale commission.
A sliding scale commission is a percent of premium paid by the reinsurer to the cedant that slides with the actual loss experience, subject to set minimum and maximum amounts.
Formula for the Expected Technical Ratio
Expected Technical Ratio = Expected Loss Ratio + Expected Commission
Explain how a “carryforward provision” works.
Suppose that past loss ratios have been above the loss ratio corresponding to the minimum commission. A carryforward provision allows the “excess loss amount” to be included with the current year’s loss in the estimate of the current year’s commission.
It is used to help smooth results over the long run
Briefly describe two approaches for pricing the impact of carryforward provisions. For each approach, identify one issue.
- Estimate the impact on the current year only – with this approach, we shift the slide by the amount of the carryforward. An issue with this approach is that it ignores the potential for carryforward beyond the current year
- Estimate the impact on a block of years – with this approach, the variance of the aggregate distribution is reduced since we assume that individual bad years will be smoothed by individual good years. An issue with this approach is that the method for reducing the variance is not obvious
Explain how a profit commission works.
Under a profit commission, a specified percentage of the reinsurer’s profit is returned to the primary insurer.
Explain how a loss corridor works.
Under a loss corridor, the cedant re assumes a portion of the reinsurer’s liability for a specified loss ratio layer.
Identify the experience rating steps for per-risk excess treaties.
- Assemble the subject premium and historical losses for several years
- Adjust the subject premium to the future level
- Apply loss trend factors to the historical large losses and determine the amount included in the excess layer being analyzed. If ALAE applies pro-rata with losses, it should be added individually for each loss
- Apply excess development factors to the summed excess losses for each historical period
- Divide the trended and developed layered losses by the adjusted subject premium to calculate loss costs for each historical period and in total
Identify an advantage of exposure rating over experience rating.
Exposure rating models the current risk profile rather than using past risk profiles.
Formula for the Reinsurer’s Expected Loss Cost
Reinsurer’s Exp. Loss Cost =
Exp. Loss for Reinsurer/Subject Premium
Briefly describe how to handle inuring reinsurance when using experience rating to price a per-risk excess treaty.
Restate the historical loss experience net of the inuring reinsurance. Then, continue with the normal experience rating steps.
Briefly describe how to handle inuring reinsurance when using exposure rating to price a per-risk excess treaty. Assume a single exposure curve is being used.
We apply the exposure rating steps directly to a risk profile adjusted to reflect the inuring reinsurance.
An actuary is pricing a per-risk excess treaty using exposure rating. A surplus share treaty inures to the benefit of the per-risk excess treaty. In addition, multiple exposure curves varying by insured value are being used in the exposure rating process.
Explain how the surplus share treaty should be handled in the exposure rating process.
Since multiple curves are being used:
* The curves should be selected based on the insured value before the surplus share is applied
* The exposure factor should apply to the subject premium after the surplus share is applied
Working Layer vs. Exposed Excess vs. Clash Cover
- Working Layer – low attachment point; expected to be pierced multiple times annually; often retained by the cedant
- Exposed Excess – excess layer with attachment point below some policy limits; these losses are less frequent than a working layer as there will be some years where no losses pierce the attachment point
- Clash Cover – high attachment point above any single policy limit; clash covers are penetrated due to losses on multiple policies from a single occurrence OR from extra-contractual obligations
An actuary is using experience rating to price a casualty per-occurrence excess treaty. As part of the pricing exercise, she trends the historical losses and caps them at the historical policy limits.
Briefly describe the issue with this approach and suggest and alternative way forward.
If we apply the historical policy limit to each loss, we fail to recognize that policy limits will generally increase over time.
As an alternative, we could apply the trend factor to the historical loss without applying a policy limit cap. In doing so, we are implicitly assuming that the policy limit increases at the same rate as inflation. If we use this approach, then the subject premium must be increased to a level that matches the inflation-adjusted policy limits
An actuary is using experience rating to price a casualty per-occurrence excess treaty.
Describe two ways in which ALAE could be handled in the experience rating exercise.
- Pro-rata with loss: ALAE in the layer is estimated in proportion to losses
- Included with loss: ALAE is added to the loss and the treaty limit applies to the sum
Four Cautions When Using Industry Information from the Reinsurance Association of American to Obtain Excess Development Factors
- The reporting lag from the occurrence of an event to the establishment of a reinsurer’s case reserve may vary by company
- The mix of attachment points and limits is not cleanly broken out in the RAA studies. This is problematic since development varies by attachment point
- The RAA data might contain Asbestos and Environmental claims which could distort development patterns
- The RAA workers’ compensation data might not include a consistent handling of tabular discounts on large claims
Briefly describe two potential loss-sensitive features of casualty per-occurrence excess treaties.
- Aggregate Annual Deductible (AAD) – cedant retains all losses in a layer up until the aggregate losses reach the AAD
- Swing Plan – the actual layer losses are loaded for expenses and the result is charged back to the cedant, subject to maximum and minimum constraints
Identify one advantage and three disadvantages of using an empirical aggregate distribution model.
Advantage – Easy to calculate
Disadvantages
1. It does not account for all possible outcomes and relies on the historical average. The actual result may differ greatly from the historical average
2. It may not properly reflect changes in business volume or mix of business
3. If losses were developed with the BF or Cape Cod method, historical losses may under-represent the true future volatility
Identify one advantage and two disadvantages of using the lognormal distribution to model the aggregate loss distribution.
Advantage – Simple to use, even when the source data is limited
Disadvantages
1. It does not allow for the loss free scenario. The lognormal distribution is not defined at y = 0, where Y is lognormally distributed
2. There is no easy way to reflect the impact of changing per occurrence limits on the aggregate losses (situation when policies have a mix of 1M or 2M per-occurrence limits)
Briefly describe the recursive calculation of the aggregate distribution.
The recursive formula is a type of collective risk model that works well for low frequency scenarios. The frequency distribution is assumed to be Poisson, negative binomial, or binomial. The severity distribution is defined in discrete, equal steps.
Identify two advantages and two disadvantages of the recursive aggregate loss model.
Advantages
1. Simple to work with
2. It provides an accurate handling of low frequency scenarios
Disadvantages
1. The calculation is more intensive for higher frequencies
2. It requires a single, discrete severity distribution with equally spaced values:
Four General Concerns When Using Collective Risk Models
- Collective risk models can be complex and feel like a “black box”
- Collective risk models assume that each occurrence is independent of the others and that the frequency and severity distributions are independent.
This may not be accurate in all cases - Some collective risk models have a large error for low frequency scenarios
- The aggregate distribution reflects the process variance of losses, but does not reflect the full parameter variance
