Q&A Bank Part 3

Question 1

Fundamental reason why statistical methods may not be appropriate when estimating claims outstanding reserves

Answer 1

The underlying assumptions my be incorrect and/or there may be a bias in the source data

Question 2

12 Possible sources of error when using statistical methods

Answer 2

• changes in the mix of business
• policy conditions may change
• insufficient data generally
• reporting delays may change
• settlement patterns may change
• large claim distortions
• past and future inflation assumptions are wrong
• further claims outstnading from earlier origin years
• secular or social trends not projected properly
• random fluctuations within the two sharp corners of the triangle are magnified by methods
• change in the average cost of claim or definition of a claim will invalidate the average cost per claim method
• if assumed run off pattern or ultimate loss ratios are inappropriate, this will invalidate the Bornhuetter-Ferguson method.

Question 3

List the circumstances in which an insurer would put more reliance on the aggregation of case estimates than statistical methods

Answer 3

New class with no past data

Where there are a small number of claims outstanding, eg:

• small class of business
• low claim frequency
• last remaining claims from a cohort

Classes with large variation in claim size.

For very large claims, especially those sensitive to court decisions over liability or compensation.

Where there is no stability over time.
Where there is no suitable mode, or the assumptions are unreliable
Where the company has a strong team of experienced assessors.

Question 4

Identify the effects of inadequate data on reserving

Answer 4

• Inadequate data could lead to either under or over-reserving
• An incorrect assessment of reserves may lead to inappropriate decisions on reinsurance

Question 5

Consequences of under-reserving

Answer 5

• Will lead to a shortfall of funds and an inability to meet liabilities as they become payable
• Will speed up the payment of dividends and tax
• May filter through to the premium rating exercise, resulting in incorrect rates

Question 6

Consequances of over-reserving

Answer 6

• Will worsen the apparent results, possibly causing a loss of confidence in the company if the true position is not considered
• Will reduce the apparent solvency margin, possibly causing problems with regulator / rating agencies.
• May lead to more caution than would otherwise be necessary possibly reducing overall returns to shareholders.
• May filter through to the premium rating exercise, resulting in incorrect rates

Question 7

4 Factors that will influence the choice of valuation method and assumptions when determining the value of an insurer’s liabilities

Answer 7

• the purpose of the valuation
• the class of business (eg more margins for long-tail, liability business)
• the size of the solvency margin
• quality, amount and stability of data

Question 8

How would one assess the need for a general insurer to set up an additional reserve for unexpired risks

Answer 8

• An insurer might need an AURR if the URR is greater than the UPR. This will arise if the premiums are considered inadequate.
• We could assess the URR by an estimated claim ratio for the unexpired period applied to the gross unearned premium.
• The claims ratio will need to be adjusted to allow for trends, inflation, changes to risk, changing policy conditions etc

Question 9

Define “anchoring”

Answer 9

The tendency to rely too heavily on one piece of information when making a decision affected by a range of factors.

Question 10

Explain the danger of anchoring when reserving.

Answer 10

There can be a danger of anchoring on past experience when setting future claims estimates even when new trends are beginning to emerge.
By not taking enough account of these new trends, the results gradually cease to be reasonable.

Question 11

3 Advantages of alternative sets of assumptions to quantify the uncertainty in a reserve estimate

Answer 11

• simple to carry out for both deterministic and stochastic models
• judgement can be exercised when considering which alternative sets of assumptions to consider
• we can exclude scenarios which we do not expect to be repeaded. This in contract to a stochastic approach where unlikely scenarios will be implicitly included in the results.

Question 12

3 Disadvantages of alternative sets of assumptions to quantify the uncertainty in a reserve estimate

Answer 12

• We cannot estimate the distribution of future outcomes unless we assign a probability to each set of assumtpions
• We ignore model uncertainty
• If a deterministic model is used with alternative sets of assumptions then it does not allow for process uncertainty.

Question 13

3 Approaches used to quantify the uncertainty in reserves

Answer 13

• alternative sets of assumptions
• stochastic modelling
• scenario testing

Question 14

8 Reasons why a loss ratio diagnostic based on paid claims has been rising over time

Answer 14

• fall in premium rating strength
• poor general claims experience
• poor claims experience as a result of a unique / large claim or a type of claim
• less stringent claims underwriting
• less stringent policy terms and conditions
• high claims inflation
• an increase in the speed of claim settlement
• if the loss ratio is net, issues linked to the reinsurer, eg default

Question 15

Possible reasons why two reserves may differ

Answer 15

• there is a different purpose to the reserving exercise
• the data used was different
• access to additional data
• different reserving methods were used
• differences of opinion
• there is an error

Question 16

Define “survival ratio”

Answer 16

A survival ratio shows how long a reserve or IBNR estimate will last if current paid or incurred claims development continues at a given rate.

Question 17

Discuss the uncertainties underlying any estimates of an insurer’s liabilities

Answer 17

• Size of payment is not known in advance (mostly)
• Different staff could produce different estimates of the liability
• Uncertainty over whether or not the claim falls within the terms of the policy
• The reinsurer may take a different view about the claim (resulting in delays and lower recoveries)
• it is difficult to predict renewals/lapses
• claims from new business are harder to estimate
• business mix and volume may not be the same as the previous years
• inappropriate chosen statistical model or parameters
• there may be errors in the data/model
• the assumptions underlying the model may no longer be appropriate

Question 18

Appropriate checks that should be undertaken to ensure that reserving calculations have been carried out correctly

Answer 18

• check for completeness of the data
• high level checks of frequency and average cost over periods of time
• compare data with that used in a previous review
• where loss ratios are used, check that claims have attached correctly to the policy data
• check that data hasn’t been corrupted in the cleaning process
• check that data has fed through correctly into reserving software packages
• check estimates against those used by other departments
• check that frequency and average cost models combine correctly
• check that frequency, inflation or any trends have been correctly project to the expected payment dates
• check that allowance for reinsurance recoveries is consistent with the reinsurance programmes in place
• check that appropriate allowance has been made for individual large claims and accumulations
• check against competitors’ reserves for similar business
• ensure that an appropriate allowance is made for claims handling expenses, or that a separate reserve has been set up for these
• check credibility of data in cells and homogeneity within cells
• check suitability of model and data cells
• check that any changes in the reserves look reasonable by comparing with previous reviews.

Question 19

Define free reserves

Answer 19

Assets ess technical reserves and current liabilities

Question 20

List 10 methods a general insurer might use to increase its level of free reserves

Answer 20

• raise capital
• weaken the valuation basis of assets
• weaken the liability valuation basis
• write more profitable business
• increase premium rates, assuming volumes remain constant
• possibly write less business
• control expenses better
• improve investment returns, both income and gains
• pay out less dividends
• possibly make use of equalisation reserves

Question 21

6 Issues to consider when communicating uncertainty in reserve estimates

Answer 21

• A numerical estimate of uncertainty should be included that gives a point estimate of reserves
• Relevant guidance should be adhered to
• actuaries should normally indicate the nature, degree and sources of uncertainty
• Consider whether it is practical to quantify the uncertainty
• Consider the need to demonstrate the uncertainty in outcome rather than a range for the best estimate
• Consider need to communicate uncertainty in a way that the intended audience will understand

Question 22

Explain IBNR provision

Answer 22

Incurred but nor reported provision:

A reserve to provide for claims in respect of events that are believed to have already happened, but still have to be reported to the insurer.

Question 23

Explain IBNER provision

Answer 23

Incurred but not enough reserved / reported provision

A reserve reflecting changes (increases and decreases) in initial estimates of claims outstanding.
For direct writers, the reserve will usually be an implicit part of the reserve for reported outstanding claims. However, reinsurers will often hold it explicitly to reflect the greater uncertainty in the original estimates provided by direct writers.

Question 24

State 4 circumstances when the IBNR may need to be calculated as a separate amount from other parts of the claim reserve

Answer 24

• when outstanding claims reserves are calculated using case estimates
• when outstanding claims reserves are calculated using statistical methods with a reporting year cohort for grouping claims
• for separate statutory returns and tax accounts where a separate statements of the IBNR is required.
• for internal management accounts where a detailed breakdown of technical liabilities may help management in their decision making processes.

Question 25

Exposure-based reserving methods

Answer 25

Exposure-based methods can be used for one-off events or risks. Two approaches used are bottom-up or top-down.

Question 26

Bottom-up approach

Answer 26

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.

Question 27

Top-down approach

Answer 27

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.

Question 28

Ratio methods

Answer 28

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.

Question 29

Components of prediction variance

Answer 29

Prediction variance = Process variance + Estimation variance

Question 30

Estimation variance

Answer 30

Reflects the fact that our best estimate is derived from a model, which will not be perfect because it may not be the most appropriate model, it is based on a finite amount of data and it may depend on other assumptions as well.

Question 31

Process variance

Answer 31

Reflects the fact that, even if we have a perfect model, because of the inherent variability in the claims process, the actual value of the reserves will almost certainly differ from the best estimate we calculate.

Question 32

Underwriting cycle

Answer 32

The underwriting cycle reflects the changes in premium rates and underwriting conditions as a result of changing levels of competition in the market.

The underwriting cycle results in market conditions fluctuating between a hard market and a soft market.

Question 33

Hard market

Answer 33

• limited capacity / supply means that premium rates are high, policy terms and conditions are more stringent and business is very profitable, leading to…
• …more companies entering the market, capacity increasing so that the increase in competition leads to profit margins being squeezed

Question 34

Soft market

Answer 34

• lots of capacity / supply means that rates are low, policy terms and conditions are less stringent and business is no longer profitable, leading to…
• … some insurers leaving the market, reducing capacity.

Question 35

Discuss the impact of the underwriting cycle on the estimation of reserves

Answer 35

Appropriate allowance needs to be made for the underwriting cycle in the reserving exercise.

Eg if the methodology is based on loss ratios, then an allowance should be made for changes in premium rates, eg by using a rating index.

Also, if the underwriting cycle has resulted in changes to policy terms and condition, then this must be allowed for in any estimated loss ratio, eg when using the Borhuetter-Ferguson method.

The development pattern is also affected by the position in the underwriting cycle.

Question 36

Explain why a stochastic reserving model might be preferred to a deterministic model

Answer 36

A deterministic model only provides a SINGLE BEST ESTIMATE of the reserve required.
A deterministic reserve gives no information about the uncertainty present in the reserve estimate.
In reality the actual amount ultimately required to pay the claims may differ from the best estimate
It is important to allow for the uncertainty in the estimates

Question 37

In reality the actual amount ultimately required to pay the claims may differ from the best estimate due to (6)

Answer 37

• variations in the occurrence and severity of claims
• notification delays
• legal changes, levels of litigiousness, court rulings
• inflation
• changes in the mix of claims
• changes in claims handling processes

Question 38

9 reasons when it is important to allow for uncertainty in the estimates

Answer 38

• for solvency purposes
• to determine capital requirements and capital allocation
• to assess reinsurance requirements
• to comply with regulations
• for investors and policyholders to compare different insurers
• when pricing insurance and reinsurance policies
• when comparing different datasets
• when monitoring performance to see if claims are reasonable
• when communicating results

Question 39

Data requirements for the Mack model

Answer 39

The Mack model has similar data requirements to the basic chain ladder method, namely:

• paid or incurred claims
• split by origin and development year
• in incremental or cumulative form
• in real amounts or money amounts

Question 40

Output from the Mack model

Answer 40

The output of the model consists of a best estimate and a standard error for the best estimate for each origin year and for all origin years combined.

The Mack model is distribution-free. It does not produce a precise distribution, although a two parameter distribution such as normal or log-normal can easily be fitted using the mean and variance.

Question 41

Bootstrapping

Answer 41

A technique for determining the statistical properties of a quantity by using the randomness that is present in a sample from the underlying population and then applying a Monte Carlo approach.

It involves sampling (with replacement) repeatedly from an observed dataset in order to create a number of pseudo datasets that are then consistent with the original dataset.

Various statistics of interest can then be derived for each pseudo dataset, and the distribution of these statistics can be analysed further.

It is assumed that the sampled data are independent and identically distributed.

Question 42

The approach to use bootstrapping techniques to estimate the distribution of reserve predictions (6)

Answer 42

This approach involves:

• obtaining a set of past claims data, split by origin / development year
• back-fiting a model to the past data to find the expected claims for each cell
• calculating the residual “noise” present in each cell
• sampling from this residual distribution to produce many pseudo data sets
• calculating reserve projections based on each pseudo dataset
• collating the reserve projections to determine the distribution moments and percentiles of the reserve distribution

Question 43

Bayesian method

Answer 43

Bayesian methods assume that the parameters in the model do not have a fixed value but themselves conform to a certain prior distribution.

If we combine an assumed prior distribution for the parameters with a model for the development of the claims, we can find the posterior distribution for the parameter.
This combines our initial beliefs about the parameter with the additional information provided by the data.

The posterior distribution can then be used (analytically) to calculate moments and percentiles for the reserves.

Question 44

4 Assumptions of Bayesian methods

Answer 44

• the run-off pattern is the same for each origin year
• the incremental claim amounts are independent and identically distributed
• the incremental claim amounts take positive values
• the variance of the incremental claim amounts is proportional to the mean

Question 45

4 Steps of the Bornhuetter-Ferguson model

Answer 45

This approach involves:

• obtaining a set of past claims data, split by origin / development year
• selecting a prior distribution to model the exposure measure
• determining the posterior distribution of the claims reserves
• using the posterior distribution to determine moments and percentiles for the claims reserves

Question 46

“Over-dispersion”

Answer 46

refers to a distribution where the variance exceeds the mean.