Chapter 25: Reinsurance reserving

Question 1

Data can be a problem particularly for reinsurers because (7)

Answer 1

• claim reporting delays are longer
• there is a greater tendency for claims to develop upwards
• exposure can be very heterogeneous
• data can be sparse
• benchmarks are often less relevant
• there can be IT constraints
• there is more opportunity to group data differently

Question 2

7 Factors to consider when grouping data for reinsurance reserving

Answer 2

• type of contract (facultative, treaty)
• type of cover (quota share, surplus, aggregate XL, etc.)
• basis of cover (losses occurring, risks attaching, claims made)
• line of business (casualty, property, marine, …)
• attachment point
• territory (Northern, Southern, …)
• type of cedant (small, large, …)

Question 3

6 Main methods reserving for outwards reinsurance

Answer 3

• 1. use data gross and net of reinsurance, then find the difference (G-N)
     —-this method uses triangulation techniques - CL, BF or even cape cod to get gross and net reserves to arrive at the reins recoveries
     —-if using BF method, then estimate gross ultimate claims and then estimate net ultimate claims in which the apriori ELR is derived by netting down the gross ELR using a net to gross ratio
• 2. perform standard triangulation techniques directly on reinsurance data alone (R)
• 3. adjust gross data using a broad brush approach (G*% ceded) using cession rates for proportional, for non proportional use paid triangles mostly esp. for short tailed and incurred or paid for long tailed)
• 4. case-by-case approach on only the largest losses
     ———Reinsurance recoveries on smaller losses are ignored completely.
     We set the reinsurance reserves on a case-by-case basis, after discussing these with claims handlers and underwriters, and perhaps with reference to any previous experience for events of that type. Typically we might reserve in this way for losses from the major property catastrophe (storm and quake) events, plus perhaps unusually large single risk events (explosions, fires and so on). This may also be a suitable approach for reserving for facultative reinsurance business.
• 5. develop all individual losses and then apply the reinsurance to each one (I-R)
     ———————This approach is the most complex and time-consuming.
     We develop each individual loss to ultimate settled value. We run each loss through all the applicable reinsurance contracts to calculate the ultimate recoveries. We track the recoveries for each contract and aggregate them so that we can apply aggregate limits and retentions. We can also calculate reinstatement and additional premiums.
     We aggregate the recoveries and premiums by line and year and compare them to paid and incurred recoveries and premiums to calculate the reinsurance reserves.
     One of the better ways to utilise this approach would be to use stochastic reserving at individual claim level, to develop the gross losses. We can then calculate a distribution of reinsurance recoveries as well as an expected value. This might be the most appropriate approach where identification of particular percentile outcomes are required.
• 6. derive a reserve distribution net of reinsurance (N)

——We can use the following simple approaches to derive a reserve distribution net of reinsurance under non-proportional covers: (also covered in stochastic reserving chapter 16)

1. Derive a gross distribution, and scale down the distribution such that the mean equals the net best estimate. Under this method, we will usually overestimate the uncertainty surrounding net reserves because reinsurance protection will dampen down the volatility associated with individual large claims.
2. Estimate a distribution of reinsurance to gross reserve ratios and apply this to the gross reserve distribution.
3. Use a net triangle rather than a gross triangle to derive the predicted distribution. Under this method, we will underestimate volatility if (for example) reinsurance retentions are increasing for the more recent origin periods and overestimate volatility if, for example, reinsurance retentions are decreasing for the more recent origin periods.
4. Simulate individual claims and net down explicitly before aggregation.

Question 4

The suitability of any reserving method can be assessed by considering

Answer 4

• simplicity
• consistency of gross and net estimates
• whether it can be used to assess volatility of net outcomes or reinsurance recoveries
• compliance with regulation
• how the method copes with:
• —- different types of reinsurance, (proportional, non-proportional, …)
• —- sparse data
• —- changes in reinsurance programme or panel over time
• —- reinsurance recoveries on unreported claims
• —- catastrophes and large claims
• —- aggregate features such as profit commissions, and loss-sensitive contracts such as stop loss cover
• —- interactions between covers
• whether the method can be used to investigate:
• —- capital requirements and enterprise risk management
• —- credit risk

Question 5

Inwards reinsurance

Answer 5

Reinsurance business sold by the reinsurer

Question 6

Outwards reinsurance

Answer 6

Reinsurance bought by the cedent

Question 7

Why do non-proportional reinsurance claims have a greater tendency for claims to develop upwards?

Answer 7

Large claims have
… longer delays to settlement so that there is
… more time for social and economic inflation to effect the final settlement amount.

Question 8

Why do reinsurers experience greater heterogeneity of exposure?

Answer 8

They may write
… a wide range of lines of business
… on a wide range of contract types with
… very different terms and conditions

Question 9

Why do you reinsurance have sparse data?

Answer 9

Particularly for high excess nonproportional business there may be
… very few actual claims.

Question 10

Why do reinsurers experience reduced applicability of industry benchmarks?

Answer 10

Because of the heterogeneity of their exposures different reinsurers can experience very different claims development behaviour.
This makes industry-wide benchmarks potentially less appropriate.

Question 11

How do re-insurers suffer from data and systems constraints?

Answer 11

The information that a reinsurer receives about losses can have less detail than the information that the insurer receives.

This is a bigger problem for proportional covers, where the cedant might report losses on an aggregate basis. For example, for a quota share written on a ‘risks attaching’ basis, the cedant might report aggregate paid and incurred losses to date. If the reinsurer uses an accident year reporting basis, it must somehow split the risks attaching data supplied between accident years.

Usually the cedant provides more information about losses to a non-proportional contract. But even then, a reinsurer may need to spend a material amount of time and resource in requesting additional information which it feels that it needs to allocate and treat the losses appropriately.

Where a reinsurance contract covers several lines of business, the loss data may show which losses are associated with which lines. But often the premium is allocated to the lines according to a pre-agreed percentage split, perhaps based on the expected split of business when the contract was underwritten. To the extent that this split differs from the actual mix of business or does not appropriately allow for different levels of risk between lines of business, the premium split may be inaccurate. As premium (adjusted for rate changes) may be the only measure of exposure a reinsurer has, this can lead to a mismatch between exposure and losses in the reserving process.
Because of the complexity and individuality of reinsurance risks, it is difficult for a reinsurer to have IT systems that capture perfectly all the contracts written and their key features.
It is more difficult than for a cedant, whose contracts tend to be more homogenous. This makes storing and accessing accurate information harder for reinsurers. The actuary working for a reinsurer should be aware of the potential shortcomings of the data being used in the calculation of reserves.

Question 12

(Outwards reinsurance) Reserving using data gross and net of reinsurance:
Advantages

Answer 12

• simple to apply and understand
• simple to add to semi-automated reserving process
• we can use it to assess the volatility of net outcomes
• appropriate for proportional reinsurance or very high excess reinsurance where there are relatively few reinsurance recoveries made.
• appropriate where the reinsurance programme has been relatively stable over a number of years
• simple to adjust the method to allow for major catastrophes

Question 13

(Outwards reinsurance) Reserving using data gross and net of reinsurance:
Disadvantages

Answer 13

• 1. possibility of implied negative reinsurance recoveries
• —————–because of over reserving in initial dev yrs on account of prudence which is later corrected with a downward trend towards the end of the dev period in the gross reserves. this may be inconsistent with the net data trend resulting in negative recoveries.
• 2. where reinsurance protections have changed it may not be appropriate to apply the “net of reinsurance development patterns prior to the change” after the change
• 3. May be less appropriate for nonproportional covers
• 4. cannot accurately allow for some features of individual reinsurance contracts such as aggregate limits aggregate retentions and profit commissions
• 5. cannot accurately allow for claims that breach the vertical cover available unless these are adjusted for separately
• 6. The lack of direct link between the gross and net experience could lead to inconsistent results for capital/enterprise risk management
     
     7. does not permit accurate assessment of credit risk
     8. may not adequately reflect changes in the gross book of business.

Question 14

(Outwards reinsurance) Applying standard reserving techniques to re-insurance premium and claims data triangles:
Advantages

Answer 14

• relatively simple to understand
• simple to add to semi-automated reserving process
• can be used to assess volatility of reinsurance recoveries and so also credit risk
• simple to adjust the method to allow for major catastrophes

Question 15

(Outwards reinsurance) Applying standard reserving techniques to re-insurance premium and claims data triangles:
Disadvantages

Answer 15

• it may be hard to assess development patterns as data can be sparse
• where reinsurance protections have changed it may not be appropriate to apply the reinsurance recovery development patterns prior to the change after the change
• changes in reinsurer panel can change payment development patterns and this method will not capture this accurately
• this approach does not allow accurately for individual contract aggregate features
• this approach does not allow accurately for individual claims breaching limits in vertical cover unless we adjust for the claims separately
• we cannot be sure that the gross and net positions are consistent

Question 16

(Outwards reinsurance) Applying broad brush features to projected gross data:
Advantages

Answer 16

• more accurate treatment of proportional business

- still reasonably simple

Question 17

(Outwards reinsurance) Applying broad brush features to projected gross data:
Disadvantages

Answer 17

• requires the ability to identify reinsurance premiums and recoveries data by cover type and line of business
• requires more information such as detailed knowledge of current and historical proportional covers

Question 18

(Outwards reinsurance) Case-by-case reserving

Answer 18

We only reserve for reinsurance on the largest most material claims.

Question 19

(Outwards reinsurance) Case-by-case reserving:

Advantages

Answer 19

• simple
• consistent with corresponding gross losses
• appropriate for catastrophe covers and high excess reinsurance

Question 20

(Outwards reinsurance) Case-by-case reserving:

Disadvantages

Answer 20

• requires detailed knowledge of current and historical reinsurance covers
• separate allowance needs to be made for recoveries on large IBNR claims
• not practical for stop loss, proportional reinsurance, or working layer non-proportional reinsurance.

Question 21

(Outwards reinsurance) Developing individual losses and applying the reinsurance programmes to them

Answer 21

We develop each individual loss to ultimate settled value.
We run each loss through all the applicable reinsurance contracts to calculate the ultimate recoveries.
We track the recoveries for each contract and aggregate them so that we can apply aggregate limits and retentions.
We can also calculate reinstatement and additional premiums.

Question 22

(Outwards reinsurance) Developing individual losses and applying the reinsurance programmes to them:
Advantages

Answer 22

• this method should be capable of treating the features of each contract accurately
• consistent with corresponding gross losses
• allows the assessment of the distribution of reinsurance recoveries
• can allow for complex programs such as for stop losses and aggregate covers as part of the process

Question 23

(Outwards reinsurance) Developing individual losses and applying the reinsurance programmes to them:
Disadvantages

Answer 23

• complex and time-consuming to set up and so not suitable for simple programs
• development of individual losses is non-trivial and not uncontroversial process
• how to allow for reinsurance recoveries for unreported claims
• requires detailed knowledge of all current and historical covers

Question 24

(Outwards reinsurance) 4 approaches to derive a reserve distribution net of reinsurance under nonproportional covers

Answer 24

• derive a gross distribution, and scale down the distribution such that that the mean equals the net best estimate
• estimate a distribution of reinsurance to gross reserve ratios and apply this to the gross reserve distribution
• use the net triangle rather than a gross triangle to derive the predicted distribution
• simulate individual claims and net down explicitly before aggregation

Question 25

Why high excess property treaty is not short tailed?

Answer 25

The fact that the business is written via a treaty means that there will be delay as potentially large losses may not be reported to the reinsurer immediately. Once a claim does hit the layer, there will be some doubt as to its ultimate value, meaning that settlement could take longer.
For example, consequential losses can be complex and time-consuming to quantify. In addition, they may be payable for a long period of time, for example until the property is rebuilt or until the policy limit is reached.
The resulting reinsurance losses are therefore unlikely to be short tailed

Question 26

What data should be used for reserving of inwards reinsurance?

Answer 26

The reasons for using a different approach than for direct business largely stem from the longer length of tail of the reinsurance business.

For a reinsurer, the incurred losses are the result of an aggregation of loss data from a number of different cedants. All these cedants will have slightly different reserving practices, and these may have changed in the past. In addition, a reinsurer’s pool of cedants may change from year to year.
The incurred data for a reinsurer will be much less consistent than for a direct insurer. The reinsurer’s claims team would have to review all the losses submitted and adjust the data submitted to make the year-by-year and cedant-by-cedant data more consistent.
As a result, it might be appropriate for a reinsurer to rely more on paid development based reserves than incurred, because the payments depend less on individual cedants and more on legal process. (For direct insurance business the reverse might be more common.) The actuary may still need to estimate a tail based on analysis of case estimates and projected number of future claims or possibly a suitable benchmark if available.

Question 27

For inwards reinsurance, which classes are short tailed?

Answer 27

1. All property business excluding high excess property treaty
2. Marine and aviation hull

Question 28

Why construction risks are medium tailed?

Answer 28

because reporting delays can be longer than for property.

Question 29

For shorter tailed inwards reinsurance, which reserving approach is appropriate?

Answer 29

For shorter-tailed reinsurance business, it might be appropriate to use reserving approaches used for direct business, such as chain ladder or perhaps even an expected loss ratio, using rate and inflation-adjusted historical loss ratios as a guide. The effort required for more complicated methods is unlikely to be rewarded with a materially different or more accurate result. We may spend time and resources more productively in improving the analysis for other parts of the reinsurer’s inwards business.

It may be best to exclude all major catastrophes from the main methodology, reserve for them separately and then add them back at the end of the process.

Question 30

For inwards reinsurance, which classes are long/medium tailed?

Answer 30

Medium-tailed reinsurance business might include construction risks, high excess property treaty, marine and non-casualty aggregate excess covers.

Long-tailed reinsurance business would typically include proportional casualty treaty, casualty excess treaty, casualty aggregate excess, casualty facultative and APH.

Question 31

For long/medium tailed inwards reinsurance, which reserving approach is appropriate?

Answer 31

We commonly use chain ladder-based methods, usually in conjunction with the Bornhuetter-Ferguson, or Cape Cod approaches, with separate treatment of major catastrophes.
The Cape Cod method uses the historical experience of some or all accident years as implied by the chain ladder method, adjusted for rate changes and claims inflation. More weight is given to accident years which the incurred chain ladder method suggests are more developed and where the premium written is higher.
There could be reserving problems for new or recently established reinsurers where the oldest development year is not yet mature.
If triangulation methods are used, a tail factor will have to be applied.

In many cases, the incurred (notified) claims development pattern is more stable than the paid claims development pattern. This is because notified claims amounts contain more information (ie the estimates of outstanding) than paid claims alone. However, this is not always the case.
In

Question 32

M1Q2 - You are the new reserving actuary for an established Lloyd’s syndicate that writes mainly product liability, directors’ and officers’ (D&O) insurance, and medical malpractice (med-mal) risks. The insurance market has been soft in recent years, resulting in poor loss ratios throughout the industry. However, careful underwriting of the D&O and med-mal books has meant that these areas of the business have outperformed the market, and have remained profitable.
Your predecessor’s approach to estimating claims reserves net of reinsurance was to: 

calculate gross reserves and net these down using net to gross ratios allow for reinsurance recoveries on individual large losses separately.
The finance director has asked you to review the appropriateness of this methodology of allowing for reinsurance recoveries. Outline the points you would make in your response.

Answer 32

Use of net to gross ratios
A reasonably simple method. [½]
The methodology is consistent with that used in previous reserving exercises. [½]
This gives a natural treatment of proportional reinsurance programmes. [½]
However, the syndicate is likely also to have individual and aggregate excess of loss covers in
place. [1]
Need to be able to identify reinsurance premiums and recoveries split by:
 paid claims and case reserves [½]
 cover type [½]
 line of business. [½]
The method requires information of current and historical covers, which adds to the data and
resource requirements. [½]
Where reinsurance cover has not changed over the period, historical net to gross ratios can be
used to estimate future net claims. [½]
However, where the level of reinsurance cover or types of reinsurance have changed, it is
inappropriate to apply broad brush ratios to estimate outwards reinsurance recoveries. [1]
This is likely to be the case here due to changes in the underwriting cycle. [½]
For example:
 reinsurers may have tried to strengthen their terms and conditions, particularly as direct
business has become less profitable [½]
 retention levels may have changed [½]
 even if retention levels have remained unchanged, the real level of coverage may have
increased due to claims inflation and judicial inflation [½]
 the rate on line is likely to have changed over the course of the insurance cycle, leading to
changes in net to gross premium ratios and reinstatement premiums. [½]
Similarly, any changes in reinsurer may cause a shift in the speed of reinsurance recovery
payments, so that a broad application of the method may distort estimated future recoveries. [½]
Therefore subjective adjustments to the historical net to gross ratios will need to be made. [1]
It will be difficult to estimate which year of account to allocate reinsurance recoveries to,
since: [½]
 the syndicate’s direct business will probably be written on a claims made basis … [½]
 … whereas any non-proportional reinsurance may be written on a different basis … [½]
… consequently it will be difficult to know what net to gross ratio to use. [½]
The method does not allow for individual claims breaching the vertical cover available. [1]
However, this can be allowed for by separating large losses out of the data and treating these
separately. [½]
When calculating reserve ranges, it is difficult to allow for the lower volatility of claims reserves
due to reinsurance. [1]
Allowance for large losses
A time-consuming approach. [½]
All losses which have (or are expected to) breach reinsurance retention limits should be stripped
out of the gross data, and ultimate reinsurance recoveries on each individual loss should be
estimated separately. [1]
The features of individual contracts can be treated separately. [½]
It is a useful approach when analysing the distribution of reinsurance recoveries. [½]
It can be complex to allow for the exhaustion of horizontal cover and aggregate programmes. [1]
It only allows for reinsurance recoveries on known reported claims. Allowance also needs to be
made for recoveries on large IBNR claims. [1]
It also requires knowledge of current and historical covers, but this should already be available
since it is required for the net to gross ratio approach discussed above. [½]
It requires monitoring of losses on a case by case basis. [½]
It is necessary to adjust for any indexation of attachment points and limits, as this will erode
reinsurance recoveries on claims with long settlement delays. [½]