Chapter 15: Triangulation methods (Best estimate reserves)

Question 1

2 Important issues when presenting reserves

Answer 1

We should:

• clearly define what we mean by our single point (or best) estimate
• attempt to quantify the likely divergence from this estimate

From another card (related):

• explain WHAT HAS BEEN ALLOWED FOR the best estimate, and WHAT HAS NOT
• ensure stakeholders understand the LEVEL OF UNCERTAINTY
• comment on the UNCERTAINTY IN THE CONTEXT AND SCOPE and purpose
• focussing on the most SIGNIFICANT ISSUES, given the purpose of the exercise
• emphasise the unusual issues
• avoid MISUNDERSTANDINGS
• be consistent with VOCABULARY used by other professionals, and explain terms

Question 2

Best estimate reserve

Answer 2

• It is a point estimate, in other words a single number, not a range of outcomes.
* the expected value of the outstanding liabilities, after allowing for all the areas of uncertainty, (ie model, parameter and process uncertainty)
• It is unbiased, ie the underlying assumptions used do not take a deliberately prudent or optimistic view.
• It is meant to be the actuary’s impartial view of the reserves with no margins, implicit or explicit, for prudence or optimism.
• It is based on sound and appropriate actuarial or statistical techniques.
• It is based on current and credible information.
• The Solvency II requirements say nothing about the skewness of the underlying distribution or its inherent volatility.

Question 3

In SAM the best estimate is characterised as (4)

Answer 3

• a point estimate
• not inherently optimistic or pessimistic
• based on sound and appropriate actuarial or statistical techniques
• based on current and credible information

nothing is said in the requirements about the skewness of the underlying distribution or its volatility

Question 4

Data required for reserving: (7)

Answer 4

• premiums
• number of claims
• dates of reporting and occurrence
• case estimates
• paid claims (gross and net of recoveries)
• other measures of exposure
• expenses (direct and indirect)

Question 5

Case estimates (for use in reserving)

Answer 5

Latest estimates of the cost of each claim of which the insurer is aware.

Case estimates may be easy to determine for some classes of business, but complex for others:

• It may be easy to determine these case estimates if the benefit is fixed, such as the compensation offered for the loss of a limb under a personal accident policy.
• When the estimation process is not so straightforward, a mechanical approach may be used, or the judgement of an experienced claims handler or legal advisor may be used.

Question 6

Claims analysis:
3 cohorts of common origin

Answer 6

• year of accident
• year of reporting
• year of underwriting

Question 7

Data required:
Premiums

Answer 7

• Earned premiums are appropriate for an accident year cohort.
• Written premiums are appropriate for an underwriting year cohort.
• A reporting year cohort would be very difficult to use in a loss ratio calculation, since premiums and claims would have to be found with the corresponding exposure.

Question 8

The overriding principle of all claims analyses

Answer 8

The need to determine the basic

• characteristics
• values, and
• trends of past data.

Consideration needs to be given to

• materiality
• homogeneity of data
• how to deal with large/catastrophic losses
• how to deal with latent claims

Question 9

Main ADVANTAGE of grouping claims data by ACCIDENT YEAR

Answer 9

All claims will stem from the same exposure cohort.
The claims will therefore have been subject to the same risk environment, although they might have arisen from policies written under different rating and policy terms.

Question 10

Main DISADVANTAGE of grouping claims data by ACCIDENT YEAR

Answer 10

• The full number or amount of claims in the cohort is not known until the last claim is reported.
• This relies on detailed claims records being maintained. (eg date of loss, date reported, payment date etc). DOL can be difficult to determine in some cases.
• Claims may arise from different premium rates or terms

Question 11

ADVANTAGES of grouping claims data by UNDERWRITING YEAR

Answer 11

• We can follow the total outcome of all policies written in each year. Follows funded year accounts.
• Similarly we can follow claims that arise from a particular group of policies that are subject to the same set of premium rates and
• use the results to test the adequacy of the premiums.
• A further advantage is that the terms, rates and conditions are often more stable by underwriting year.
• IBNR and clams from unearned exposures are automatically included in the projection.

Question 12

DISADVANTAGE of grouping claims data by UNDERWRITING YEAR

Answer 12

It will take more than one year before all the claims under that cohort have occurred.
Reporting delays, including IBNER, will extend this further.
Thus takes longer to gather data.

Question 13

ADVANTAGE of grouping claims data by REPORTING YEAR

Answer 13

No further claims will be added to the cohort after the end of the origin reporting period.

Question 14

DISADVANTAGES of grouping claims data by REPORTING YEAR (3)

Answer 14

• Projection methods based on this cohort will not allow for the IBNR. A separate allowance will therefore be needed for IBNR claims.
• Claims will have come from several different exposure periods, each of which may have differed in respect of volumes of business, cover applying, claim settlement patterns and claim environments.
• It is difficult to find an exposure base that would correspond to the definition of risk under the claims being developed.

Question 15

Development period

Answer 15

The period or frequency at which each claim cohort is tracked over time.
Annual and quarterly periods are the most commonly used.

Question 16

3 Methods of estimating the outstanding claims reserves

Answer 16

• case-by-case basis
• statistical methods
• exposure based reserving

Question 17

2 Methods for deriving estimated ULTIMATE VALUES for LARGE LOSSES

Answer 17

• claims development methods
  eg. chain ladder methods, but project from the date of actual loss and allow for different speed of development
• exposure based methods

Bottom up

Top down

Question 18

Considerations in deriving ultimate values for catastrophe losses

Answer 18

Catastrophe losses often tend to DEVELOP MORE QUICKLY than attritional claims.
The main reason for this is the increased focus on these claims from claims adjusters and policyholders due to the magnitude of the losses.

Once claims experience starts to emerge, the development pattern of similar catastrophes in the past may assist the actuary in refining initial estimates.

Question 19

2 approaches to Exposure based methods for estimating ultimate values of large losses

Answer 19

• Bottom-up approach
• Top-down approach

Question 20

BOTTOM-UP APPROACH to exposure-based methods for estimating the ultimate values of large losses

Answer 20

Examine on a policy by policy basis to determine the likelihood of whether each policy is exposed to the loss event.
If they decide the underlying insured is exposed to the relevant event, a claims expert needs to assess the extent of any claim on that policy.

Question 21

TOP-DOWN APPROACH to exposure-based methods for estimating the ultimate values of large losses

Answer 21

We attribute the total market loss from an event to an individual insurer or policy level, based on the policy terms, excesses and limits.

Question 22

3 Bases on which business is written

Answer 22

• Losses occurring
• Claims made
• Risks attaching

Question 23

Losses occurring basis

Answer 23

The policy provides cover for losses occurring in the define policy period, no matter when they are reported.

This is consistent with an accident year approach.
Such policies are thus subject to potential problems in defining the date of loss which may be established as a result of legal action.

Question 24

Claims made basis

Answer 24

The policy covers claims reported during a certain period.

It is used to reduce the tail on liability business by removing the development caused by late reporting.

Question 25

Risks attaching basis

Answer 25

A basis under which reinsurance is provided for claims arising from policies incepting during the period to which the reinsurance relates.

This is consistent with an underwriting year approach.

Question 26

5 ways in which to apply benchmarks

Answer 26

We can apply benchmarks in different ways, including:

• incremental development factors
• paid or incurred to ultimate factors ultimate loss ratios
• IBNR as a percentage of paid, outstanding or incurred
• IBNR as a percentage of premium.

An age-to-age development factor is just the development factor as calculated in the standard basic chain ladder method approach. But here we would adjust the factors obtained from our own data by comparing them with the corresponding benchmark data.

Question 27

Age-to-age development factor

Answer 27

The development factor as calculated in the standard basic chain ladder approach.
But here we would adjust the factors obtained from our own data by
… comparing them with the corresponding benchmark data.

Question 28

Issues that affect the stability of the claims development pattern (11)

Answer 28

• distortions in the data
  due to changes in (administration) processes can affect the normal claims development.
  Such changes could involve stricter claims underwriting or a new system to speed up the claims processing. Such changes affect the size and speed of the run-off respectively.
• claims reviews
  It is common for companies to undertake periodic claims reviews to ensure that the case reserves being held accurately reflect all currently known information relating to the claim. If such reviews are carried out regularly then it might be reasonable to assume that the historical development reflects the average impact that such reviews have, and that the future development may follow a similar pattern.
  However, if such reviews are infrequent, or if a large ‘one-off’ review has been carried out, or if the company undertakes the reviews more frequently than it has in the past, it may be necessary to adjust the development pattern derived from the data.
• market wide initiatives
  For example, a market-wide initiative was put in place to speed up the reporting of energy losses arising from damage to oil rigs, following hurricanes in the southern US and Gulf of Mexico during 2005.
  If such initiatives are taken, it is important that any chain ladder model that is fitted to the data recognises that the claims development may be different from what may be typically expected for the type of business or loss in question.
• seasonality:
  Seasonality can affect the claims development pattern, both within a cohort and for one cohort relative to another where the exposure period is not the same. Seasonality is the tendency for certain types of policy to have more claims at certain times of the year. For example, motor policies usually have more claims in winter when the weather conditions are more hazardous and household insurers receive more subsidence claims in the autumn / winter following a hot summer. Seasonality may not have a bearing on annual development factors but quarterly factors may appear less than smooth.
  Seasonality can also impact the speed at which claims are processed – for example, fewer claims may be processed during December when there are a greater number of bank holidays.
• developments in the business, economic and legal environment.

changes in:
- terms and conditions
- mix of business
- claims handling processes
1. Changing practices regarding the point at which a notified loss is formally accepted as a claim by the company and is marked as such on the claim file.
2. A new claims process is implemented that speeds up the processing of newly notified claims.
3. The case reserving philosophy is changed. For example, from ‘best estimate’ to ‘realistic worst case’, or if the initial standard case reserve is changed for certain types of claim.
4. A change in the period before non-active claims are reviewed – either to chase for outstanding information or to close the claim as a nil claim.
5. Delays in making claims payments, whether deliberate or due to circumstances.
6. The failure to mark claim records as settled on a consistent basis.
One way to deal with the first three examples might be to base the chain ladder link ratios only on development data from after the new procedures came into effect. Alternatively, we may make subjective adjustments to allow for the fact that the future development is expected to be different from that suggested by the historical data.
We may deal with the last two examples by excluding the affected link ratios.
- commencement of writing policies
- average policy length
- reserving policy

Question 29

Issues affecting claims development stability:
Changes in the mix of business

Answer 29

Changes in the mix of business will increase the heterogeneity in the data.

Question 30

Re-underwriting

Answer 30

Sometimes an insurer will state that they have "re-underwritten" a class of business. 
This may be for: 
- a generally poor performing class of business, or 
- a class which has suffered material losses from a single event which led to claims from a large number of policies.

Question 31

Chain ladder method

Answer 31

A statistical method of estimating the ultimate value of a set of development data, whereby a weighted average of the past development is projected into the future.
The projection for successive periods of future development is based on the actuary’s calculation of ratios of cumulative past development.

Question 32

Basic chain ladder assumption

Answer 32

1. The claims environment is stable
2. There are no shocks to the claims development
3. The weighted average inflation experienced in the past is applicable to the future
4. assumes that the pattern of claims development derived from the past experience will continue in the future.
5. First cohort is fully run-off and if not, a tail factor that is assumed is appropriate

Question 33

Method for carrying out a basic chain ladder calculation (4)

Answer 33

• Tabulate claims on a cumulative basis by development year / origin year
• calculate the development ratios
• apply these ratios to complete the table
• from the cumulative results, find the amounts expected to be paid in each future development year / origin year cell.

Question 34

Subrogation recoveries

Answer 34

If an insurer indemnifies against a loss, it may be entitled to attempt to recover som or all of that loss from a third party.

Question 35

5 key strengths of the chain ladder method

Advantages of Chain Ladder

Answer 35

• the method can be applied to a wide variety of sets of data
• provided the data can be arranged into a development triangle, the chain ladder method can be used to project it to ultimate
• the basic method can easily be modified to allow for data distortions
• the method is conceptually straightforward and it is easy to relate results back to the pattern of development
• the method can be developed to serve as a starting point for a number of other methods, eg the Bornhuetter-Ferguson method.

Question 36

3 Key weaknesses of the chain ladder method

Answer 36

• Results can be distorted by unusual experience
• Limited use for recent cohorts, particularly for long-tailed classes
• Considerable care is needed in applying the method to prevent unusual features in the data having a significant impact on the result

Question 37

Statistical methods of estimating outstanding claims might be impaired by distortions.
8 Causes of problems

Answer 37

• errors in the data
• inflation
• large claims
• latent claims
• catastrophes
• changes in procedures
• changes in the mix of business

Question 38

Loss ratio

Answer 38

The cost of claims per unit of exposure.

Question 39

Advantage of the expected loss ratio method

Answer 39

Some key advantages of this method are:
it is a simple method to apply can be used when data is sparse, unreliable or missing altogether
it is not distorted by anomalous data. This can particularly have an impact for longer tailed business and at early durations if claims experience to date is particularly light or heavy.

When to use the method
The method is simple to apply and is especially useful when the data is sparse, unreliable or missing altogether – for example, if a company has started to write a line of business for the first time. It is a simple way to check other methods.

Question 40

7 Disadvantages of the expected loss ratio method

Answer 40

• It ignores the pattern of claims development to date
• It is difficult to adjust for large claims
• If loss ratios are derived from past years, the method will replicate past biases
• The benchmarks used may not be appropriate as the business written may be different from that to which the benchmarks relate.
• Where used, the ultimate loss ratios for previous years may be understated or overstated because of fluctuations in experience.
• The underlying assumptions can be subjective.
• Where premium rate changes are introduced, these are often only for renewed business and not for new business.

Question 41

Bornhuetter-Ferguson method

Answer 41

The Bornhuetter-Ferguson method can be thought of as a credibility estimate, based on a weighted average of an expected level of claims as estimated by the loss ratio method, and a projection of the ultimate claims based on experience to date as estimated by the chain ladder method.

It combines the advantages of the loss ratio method with the advantages of the chain ladder method.

Steps:

1. Determine an initial expected ultimate claim amount for the orgin period. Eg. LR*WP, say 120.
2. Determine what proportion is developed and what is yet to be developed as per the claim ladder estimation. say d% and (1-d%).
3. use the (1-d%)*120 to get the estimated future incurred or paid claims.
4. Final expected ultimate claims is the current value of the claims (C) (incurred or paid to date) plus the expected value of the undeveloped incurred/paid claim. i.e. C+(1-d%)*LR*WP

Question 42

When to use the Bornhuetter-Ferguson method

Answer 42

• where the available data for the particular cohort is sparse
• where premium volumes are so small that the claims activity is expected to be extremely volatile
• when a blend of experience and an exposure-based estimate is deemed appropriate

The BF method is very useful where the available data for the particular cohort is sparse. This is often the case with more recent cohorts, cohorts from longer-tailed portfolios (for example, liability excess of loss reinsurance) or where premium volumes are so small that claims activity is expected to be extremely volatile.
It can also be used when a blend of experience and an exposure-based estimate is deemed appropriate.
The BF method is most effective when the current data is too immature to be developed on a projection method, but we believe the experience data to date still gives some indication of the level of ultimate claims. This is particularly the case when the experience to date has been particularly poor, but the remaining development is expected to be in line with initial assumptions.
In some cases, the data being projected may develop with a negative tail and the BF should not be used for origin periods where the percentage developed is over 100% because the assumed percentage developed is unsuitable as a weight in this credibility method. In these circumstances, the BF method would produce an estimate outside the range between the chain ladder method and the a-priori assumption.

Question 43

Main strength of the Bornhuetter-Ferguson method

Answer 43

It can be used when the claims data is at a very early state of development.

Question 44

Main weakness of the Bornhuetter-Ferguson method

Answer 44

1. It can be difficult to gather the information for the prior estimate for the claims.
2. result can be heavily dependednt on the prior estimate
3. provides little benefit over the claim ladder method for more developed origin years
4. care needed for negative claims development

Question 45

Average cost per claim method

Answer 45

A family of methods, generally estimating 2 components for each origin year:

• the claims frequency,
• the claims severity

Question 46

7 Strengths of the ACPC method

Answer 46

• Easy to understand and communicate
• Provides information about how both claim numbers and claim amounts are expected to develop in the future
• For direct business in particular, the data required is generally available
• Can be used in conjunction with other projection techniques, such as chain ladder and Bornhuetter-Ferguson.
• Helps explain volatile data and results when the data contain only a small number of claims
• Can be applied to settled claims when claims reserving protocols have changed over the development history, making some other methods invalid.
• If used in the correct way, it can be useful as a basis for estimating latent claims because we can make explicit assumptions about the average claim size, the long-term effect of inflation and the expected number of claims.

Question 47

4 Weaknesses of the ACPC method

Answer 47

• Can be distorted by reopened claims, nil claims or partial payments
• Assumes that the distribution of claims is the same for each origin year or settlement year
• Needs more detailed information, which may not always be available
• Small data samples may lead to volatile results

Question 48

Communication of the best estimate (3)

Answer 48

• Results should be explained clearly and effectively to key stakeholders
• Highlight that best estimate is just an estimate
• Highlight key assumptions and comment on the main restrictions or shortcomings in analysis.

Question 49

Incurred claims might mean (2)

Answer 49

• paid claims + estimates for outstanding reported claims
• paid claims + estimates for ALL outstanding claims (including a loading for IBNR)

Question 50

5 Examples of changes in claims handling procedures which might affect claims development

Answer 50

• Changing the point at which a notified loss is accepted as a claim
• Speeding up processing of notified claims
• Case reserving philosophy is changed
• Delays in claims payments
• Failure to consistently mark claim records as settled

Question 51

How might market-wide initiatives affect claims development

Answer 51

From time to time a major issue might arise that the market is keen to quantify as quickly as possible.

E.g. introducing compulsory 3rd party motor insurance would impact motor comprehensive claims experience.

Question 52

What is meant by claims seasonality

Answer 52

Seasonality is the tendency for certain types of policy to have more claims at certain times of the year.

Question 53

3 Examples of distorting effects on the loss ratio

Answer 53

• A catastrophe
• Change in premium rates
• Insurance cycle

Question 54

strengths and weaknesses of the Chain Ladder Method

Answer 54

“Strengths:
1. Straightforward to calculate using spreadsheet
2. Simple to use
3. and no specialized software is typically needed
4. Flexibility is available for judgement should any year need to be excluded
5. Works well if data is stable and can be triangulized by either AY or UW or reporting year.
and it has homogenous set of information
6. Easy to communicate and explain to non-technical audience
7. Widely used by actuarial professionals
Weaknesses:
1. Requires exercise of judgment on which years to include and which to exclude
2. Works well only when the experience is stable.
3. Any distortion to the experience due to large events or change in payment patterns or claim cllassification makes it less useful for reserving for the future
4. Does not work well with sparse data eg. data in a new company or new line
5. Assumes that past experience is a good indicator of the future which is not always the case.
6. It may not be useful for hte recent cohorts for a long tailed line of business”

Question 55

“Suggest appropriate method of estimating outstanding claims for each of the following classes of business
X3.9”

Answer 55

“(a) Private motor –

a. Private motor policies are personal lines policies sold in high volumes by an insurer
b. Chain ladder and other triangulation methods are appropriate given the volume of data
c. Case estimates will be slow and may not provide much value/accuracy and is generally not appropriate.
d. For large bodily injury claims, very high property damage claims case estimates can be used.
e. Categories generally can be homogenously divided for most insurers as per coverage, gender, region, type of vehicle etc.
f. and experience is generally stable over the years
(b) Mortgage indemnity guarantee:
a. Does not have a regular, stable claims experience as risks are cyclincal.
b. Claims occur during economic depression and adverse situations
c. Traditional triangulation could be problematic
d. Given the involvement of economic variables, stochastic methods are appropriate.
e. ELR method may be appropriate after consulting experts in the field.
f. Case estimates is not feasible in most cases as insurer may not have information about individual borrowers and only the mortgage provide may have that information.
(c) Employer’s liability
a. Long tailed business characterized by reporting delays
b. This is a big book for insurers and hence data may be available justifying use of statistical methods for most of the smaller claims.
c. Chain ladder may be appropriate for older cohorts.
d. For latent claims and very large claims, case by case reserving may be more appropriate than regular triangulation methods.
e. For recent cohorts, BF method may be useful to understand emerging experience.”

Question 56

A2021, Q6:
(i) Describe latent claims using an example. [2]
(ii) Outline the issues an insurer is likely to face when reserving for latent claims.
[2]
(iii) Describe, using a numerical example, the Bornhuetter–Ferguson (BF) method
for IBNR estimation. [4]
A general insurance company started writing a new Employers’ Liability (EL) line of
business 2 years ago. The company is aware that this line of business could have
exposure to latent claims.
The Reserving Actuary of the company is using the Chain Ladder method for the first
origin period, and the BF method for the most recent origin period, for the estimation
of IBNR claim reserves for the EL line of business.
(iv) Assess the impact of the choice of reserving methods on the adequacy of the
IBNR reserves for this EL line of business. [4]
[Total 12]

Answer 56

(i) Latent claims are those claims that result from those perils which were unforeseen at the time of underwriting [1]
and for which the potential for claims to be made many years later has not been appreciated. [½]
In common parlance, latent claims are also those that generally take many years to be reported. [½]

These are not reflected in the past claims data [½]
Most of these arise from diseases caused by products or industrial processes [½]
but faulty construction of buildings is another possibility [½]
Sometimes court rulings, or late disease diagnosis can trigger these claims, and can lead to significant adverse financial impact on the insurer, [½]
Suitable example with explanation e.g. asbestos, pollution claims, VWF, NIHL, Stress, Mobile phone radiation, sexual molestation of children etc. [1]
[½] mark for name, [½] mark for explaining how it is latent
Any other suitable points [1]
[Marks available 6, maximum 2]
(ii)
Many reserving techniques are based on projecting past claims development into the future [½]
or use a pricing assumption to come up with an estimate for the expected performance of the portfolio [½]
Neither can generally be used for latent claims since by definition, latent claims are not reflected in the historical data, or pricing assumptions [½]
Latent claims can have a calendar year effect [½]
Single risk can give rise to multiple claims [½]
Social trends can also influence the incidence of these claims, which can be difficult to track and allow for [½]
Date of loss may not be uniquely defined, especially for disease related claims [½]
Any actuarial estimate of reserves can therefore lead to under or over-reserving [½]
This is particularly a challenge before the latent claim is discovered [½]
but could still be a challenge post-discovery while the industry practice and exposure is being established [½]
due to which it may be challenged by regulators, auditors and senior management
more so than, for example, reserving for attritional claims [½]
Any other suitable points [1]
[Marks available 6½, maximum 2]
(iii)
The BF method is a credibility estimate, based on a weighted average of an expected level of claims [½]
estimated by the loss ratio method [½]
and of claims based on the experience to date [½]
assuming a development pattern of claims using the Loss Development Factors as would be used in a Chain Ladder method [½]
We can equally apply the BF method to paid claims or incurred claims [½]
It combines the advantages of the chain ladder method with the advantages of the loss ratio method [½]
Suitable numerical example, covering the following elements:
Chain ladder % developed [½]
ELR and an exposure measure [½]
BF Ultimate = Incurred+ ELR*Exposure*(1-% dev) [½]
IBNR = Ultimate – Incurred [½]
Max [2] marks if no example provided
Max [2] marks if only numerical example provided with no explanation
[Marks available 5, maximum 4]

Question 57

Earned reserves

Answer 57

Insurance companies are required to hold reserves on their balance sheets to cover the expected cost of paying out all claims for claims that have occurred, regardless of whether they have been reported to the insurer or not. This is commonly referred to as the earned reserves.

Where a reserving exercise is completed on an accident year basis, it will produce an estimate of the earned reserves.

Question 58

What does distribution of possible outcomes mean? How does ENIDs get considered in the Best Estimates?

Answer 58

The ‘distribution of possible outcomes’, in general, includes all reasonably foreseeable events based on the exposures of the insurer. Under Solvency II, allowance is required for ‘all possible outcomes’ which would cover emergence of new claim types and those an insurer has never previously experienced. Such claims are often referred to as ‘events not in the data’ (ENIDs). For the purposes of best estimate reserving, the allowance for ENIDs is usually considered as part of the conversion to Solvency II basis reserves.

Question 59

Problem with definition of Incurred claims

Answer 59

Note that you need to be careful over the definition of ‘incurred claims’ in this context. For example, incurred claims might mean: 
paid claims plus estimates for outstanding reported claims (eg case estimates) 
paid claims plus estimates for all outstanding claims (including an appropriate loading for IBNR).
Both of these approaches are sometimes described as using data for ‘incurred claims’. The first approach is more common, ie if given an ‘incurred claims’ data table without any guidance as to the definition used, it is probably more likely to have been prepared without any IBNR allowance. Note that if the second approach is taken the method is merely projecting the corrections to earlier estimates, whereas the first approach largely projects the IBNR.
In an exam, you may need to define exactly what you mean by incurred claims at the start of your answer.

Question 60

We have seen that reserves produced using a ‘reporting year’ run-off triangle will not include IBNR reserves. Explain what reserves are produced by a run-off triangle which uses ‘year premium written’ (or ’underwriting year’) as the claim cohort.

Answer 60

The fully developed square will include the claim payments in respect of all premiums written up to the end of the latest year (eg up to and including 31 December 2018 in the examples above). Therefore, the reserve for unexpired risks will also be included in the future development, as well as the reserve for outstanding claims. The answer is: 
 
outstanding claims including IBNR, IBNER and reserve for reopened claims unexpired risk reserve
claim payment expenses if the plotted claim data includes claim expenses.

Question 61

State the two main approaches to estimating outstanding claims. Identify which of the two should be used for estimating IBNR and which is more likely to benefit from actuarial input.

Answer 61

The two main approaches are:

1. Estimates of individual outstanding reported claims.
2. Statistical estimation of totals.

Use statistical methods for IBNR.
Actuarial input is more likely to be used in statistical estimation of totals.

Question 62

Practice Q. 15.16 :
Explain the terms IBNER provision, IBNYR provision and IBNR provision.

Answer 62

Incurred but not enough reported (IBNER) provision
A reserve reflecting expected changes (increases and decreases) in estimates for reported claims only.
[1⁄2]
For direct writers, the IBNER reserve will usually be an implicit part of the IBNR reserve. However, reinsurers will often hold it explicitly to reflect the greater uncertainty in the original estimates provided by direct writers.
Incurred but not yet reported (IBNYR) or ‘pure IBNR’ provision
A reserve to provide for claims in respect of events that are believed to have already happened, but have still to be reported to the insurer.
Incurred but not reported (IBNR) provision
A reserve to provide for the additional cost of settling all claims that occurred before the accounting date above the value of the claims incurred to date.
This is the sum of the IBNER and the IBNYR provisions. Sometimes the term IBNR may be used to refer to just the IBNYR (or ‘pure IBNR’). (

Question 63

Practice Q. 15.16 :
State circumstances when the IBNYR may need to be calculated as a separate amount from the other parts of the claim reserve.
[

Answer 63

Separate IBNYR

1. When outstanding claims reserves are calculated using statistical methods with a reporting year cohort for grouping claims.
2. For separate statutory returns and/or tax accounts where a separate statement of the pure IBNR may be required.
3. For internal management accounts where a detailed breakdown of technical liabilities may help management in their decision making processes.

Question 64

Practice Q. 15.16 :
Describe, with reasons, the circumstances under which statistical methods would not be suitable for calculating outstanding claims reserves of a general insurer.

Answer 64

When statistical methods are not suitable
Statistical methods would not be suitable when reserving for either:
1. one-off large claim events, such as a major tsunami insurance of non-standard risks, such as a satellite launch.
This is because the characteristics of the claim event or risk will be so different from the past experience that it really has to be considered on its own merits.
2. Neither would statistical methods be suitable for types of claims where the claim development is very unpredictable …
…. for example, asbestos, pollution and health hazards.
The uncertainty of claim development patterns makes the assumptions underlying statistical methods invalid.
3. Statistical methods will not be possible if past data is insufficient. [1⁄2]
4. They may also be unsuitable when there have been major changes that would be difficult or impossible to allow for, such as changes in cover, underwriting or mix of business.

Question 65

Practice Q. 15.16 :
Describe two methods that can be used to calculate claim reserves where statistical methods are not suitable, giving two examples of each method.

Answer 65

Reserving methods
1. Exposure-based methods
Exposure-based methods can be used for one-off events or risks. Two approaches used are bottom up and top down.
(i) Bottom up involves examining the conditions of each policy to determine whether the insurer is exposed to the loss event.
For any policies where the company is exposed to the risk, a claims expert will assess the extent of any claim on that policy.
(ii) The top down approach involves estimating the total market loss from an event.
We then estimate how much of this is attributed to an individual insurer (or policy) by considering the conditions (eg excesses or limits) of the policies.

2. Ratio methods
   Ratio methods can be used where there is insufficient data to use exposure-based methods. [1⁄2]
   For example, we could use survival ratios so that the reserve held is such that the company is able to sustain the current rate of claim payment or increase to reported claims for a given number of years.

Another example is IBNR to outstanding claim ratios. This involves applying a pre-determined ratio to the outstanding reported claim reserve to determine the IBNR claim reserve

Question 66

Practice Q 15.19:
A general insurance company writing only direct lines of business, has an accounting year-end date of 31 December. For the purpose of estimating the provisions for outstanding claims required for its accounts as at that date, it has decided to take into account all claims information recorded up to the end of the following month.
(i) (ii) List the main advantages and problems of adopting this course of action

Answer 66

(i) Advantages and disadvantages
The main advantages are: 

it gives a better knowledge of outstanding claim values and IBNR, including those for exceptional year-end weather claims it avoids December backlogs due to holidays, postal delays, etc
The main disadvantages are: 
   (ii) [1⁄2]. [1⁄2] claims belonging to the next financial year must be excluded claims must still be accounted for according to their status at the year end
statistical development patterns may be distorted, with subsequent difficulties for projections of IBNR, etc
preparation of statutory accounts and results may be delayed.

Question 67

Practice Q 15.19:
Outline the relative suitability of case estimates and statistical methods for calculating the provisions for reported claims in each of the following classes of business: (a)
liability
(b) (c)
property motor.

Answer 67

Suitability of case estimates and statistical methods
Applying to all three classes, case estimates have the following advantages: 
 (a)
they give greater management control over total claims reserves they pick up new trends more quickly than statistical methods.
Liability
There will normally be a relatively large number of small claims, settled quickly and a smaller number of large claims, often subject to long delays in discovery and/or settlement. Statistical methods may be necessary in the early development periods, when relatively little information is available on the larger claims.
At later durations, case estimates may deal best with the few cases then outstanding. (b)
Property
Statistical methods will normally give stable results for personal lines with large numbers of relatively small claims. Case estimating is relatively expensive in such cases.
Motor [1]
Larger claim size risk groups, such as commercial fire, may be better suited to case estimating. [1⁄2] (c)
At early stages of development, large numbers of property damage claims will make statistical estimates suitable.
At later stages, there will be relatively small numbers of large injury claims, for which case estimates may become more suitable.
[

Question 68

Practice Q 15.19: 
Outline methods for calculating the provision for IBNR claims: (a) in a class of business where claims are reported quickly and the required provision is likely to be small 
(b) in a class of business where the required provision is likely to be substantial.

Answer 68

Methods for IBNR
In both cases, if a statistical method has been used for reported claims, it may implicitly include the IBNR.
[1⁄2]
(a) In a class of business where claims are reported quickly and the required provision is likely to be small simple methods will suffice.
For example: 
 
a percentage of premiums a percentage of claims paid
a percentage of claims reported.
(b) In a class of business where the required provision is likely to be substantial more elaborate methods should be employed.
These would be based on historical development / delay patterns.
For example: 
 chain ladder techniques projection of claim numbers and average amounts. Under both methods, allowance should be made for any special features.
For example: 
 changes in claim administration [1⁄2]
[1⁄2] [1⁄2] [1⁄2]
[1⁄2] [1⁄2]
[1⁄2] [1⁄2]
[1⁄2] [1⁄2]
special claims, etc. [1⁄2] [

Question 69

Berquist Sherman method

Answer 69

Berquist-Sherman method
The results of the basic chain ladder method may be inaccurate if there have been changes to the speed of claim settlement over time.
Berquist and Sherman suggest techniques for adjusting historical development for changes to the rate of settlement (ie payment) of claims and/or changes in case reserving adequacy. These techniques produce adjusted development patterns that are consistent with the reserve adequacy levels and settlement rates that are thought to apply at the time of the latest diagonal. We derive these adjusted development patterns by restating the historical development data to be on the current reserving or settlement basis.
For example, we restate the paid claims in the triangle by examining the historical incremental claims settlements and restating the paid data such that they are consistent with the current estimated settlement rate. Similarly, we restate the incurred claims by assuming that the historical level of case reserve adequacy is the same as the current level except for claims inflation trends. We can then build up a restated incurred triangle by multiplying the restated average outstanding claim size by the number of open claims and adding the paid triangles.
We need these adjustments to ensure that selected development patterns are not distorted by shifts in the data. For example, if we believe the settlement rate has significantly increased then by projecting unadjusted paid data we would overestimate the ultimate value. This is because the unadjusted data will include a higher proportion of settled claims than before.
Practical use of this method is relatively limited as the method requires a lot of additional judgements to be made around the case strength adequacy.

Question 70

Chain ladder extention
Curve fitting
Trend analysis

Answer 70

CURVE FITTING:

If the selected development factors are to be used to project expected future development for use in actual versus expected comparisons, it is important that the development factors follow a smooth pattern. If the development curve is not smooth (for example, there are link ratios just above and below one) this can generate spurious expected movements. If care is not taken to smooth out the tails of development curves, judgemental adjustments may be needed to ensure the expected movements are sensible.
If development patterns are not smooth in the tail, this can generate small / immaterial reserves or IBNR that are not expected to be needed. It is common to set link ratios to precisely one in the tail where they are not needed to avoid noise in the pattern generating reserves or IBNR unintentionally.
Using regression techniques, we can fit curves to premium or claim development data to assist in either projecting development factors beyond the oldest development periods, and/or deriving smooth development factors. We can fit a number of different distributions, for example, Weibull, inverse power and exponential. This would involve estimating a best fit to cohort development data. We can also use curve fitting to smooth development patterns or to select a tail factor to allow for development beyond the oldest development period
When selecting the type of curve to be fitted it is important to select a curve with the appropriate degree of tail heaviness for the type of claim being modelled.
It is important when fitting curves to ensure this bears resemblance to the original data that it is intended to be fitted to. Curve fitting using regression techniques is not intended to be a substitute for applying the chain ladder methodology where data can be used.

TREND ANALYSIS:
Trend analysis
The pattern of development may change between cohorts and development periods over time. It is possible to use various ad hoc methods to quantify these trends to increase the accuracy of estimates.
For example, we can fit curves from one distribution to each cohort and then analyse the change in parameters to see if there are any trends. By carrying out a numerical review of link ratios we may observe trends, for example, faster development of claims in more recent cohorts.
The

Question 71

Circumstances when statistical methods are not suitable

Answer 71

“Statistical methods would not be suitable when reserving for either:
• one-off large claim events, such as a major tsunami
• insurance of non-standard risks, such as a satellite launch.
This is because the characteristics of the claim event or risk will be so different from the experience that it really must be considered on its own merits.
Neither would statistical methods be suitable for types of claims where the claim development is very unpredictable … for example, asbestos, pollution and health hazards.
The uncertainty of claim development patterns makes the assumptions underlying statistical methods invalid.
Statistical methods will not be possible if past data is insufficient.
They may also be unsuitable when there have been major changes that would be difficult or impossible to allow for, such as changes in cover, underwriting or mix of business.”

Question 72

Two methods that can be used to calculate claim reserves where statistical methods are not suitable

Answer 72

“Exposure-based methods
Exposure-based methods can be used for one-off events or risks. Two approaches used are bottom up and top down.
Bottom up involves examining the conditions of each policy to determine whether the insurer is exposed to the loss event. For any policies where the company is exposed to the risk, a claims expert will assess the extent of any claim on that policy.
The top down approach involves estimating the total market loss from an event. We then estimate how much of this is attributed to an individual insurer (or policy) by considering the conditions (eg excesses or limits) of the policies.
Ratio methods
Ratio methods can be used where there is insufficient data to use exposure-based methods. For example, we could use survival ratios so that the reserve held is such that the company is able to sustain the current rate of claim payment or increase to reported claims for a given number of years. Another example is IBNR to outstanding claim ratios. This involves applying a pre-determined ratio to the outstanding reported claim reserve to determine the IBNR claim reserve.”