Important

Question 1

Describe “seasonality” in the context of a reserving exercise, giving three examples

Answer 1

Seasonality is the tendency for certain aspects of the claims experience to vary over the course of the year
[½]
This can include frequency of certain types of claim [½]
…Exposure to particular perils [½]
…Severity of certain types of claim [½]
…Reporting delays [½]
…Claims processing delays [½]
Seasonality may not have a bearing on annual development factors but may ensure that quarterly factors appear less than smooth. [1]
Examples could include (credit for other valid):
Increased motor claims during winter due to hazardous conditions [½]
Increased subsidence claims during summer due to hot conditions [½]
Burst pipe claims during winter due to freezing conditions [½]
Reporting or processing delays around Christmas or other holidays

Question 2

List the main features of stop loss reinsurance.

Answer 2

Features of stop loss reinsurance:
 treaty for class or classes
 non-proportional
 reinsurer pays when total claims in the period (year) exceed an agreed level (loss ratio)
 cover may be for a proportion of claims only
 unusual unless some link between direct writer and reinsurer …
 … or where reinsured has little/no influence over underwriting and claim settlement (eg crop insurance)
 as cover is against all adverse experience (eg poor underwriting, large claims, catastrophes, poor experience, poor claims settlement), it could be expensive.

Question 3

Explain how financial quota share can benefit an insurer

Answer 3

Financial quota share is a quota share arrangement under which a generous commission payment
is made from the reinsurer to the insurer at the outset.
Under normal circumstances, the commission payment should cover:
 commission payments incurred by the insurer (return commission)
 the work of attracting and administering the business (override commission).
Under financial quota share, the initial commission may significantly exceed these components.
The surplus amount can be used in order to:
 help cover new business strain
 finance a particular strategy, eg the take-over of another insurer
 improve the solvency position of the insurer.
In future years, the commission payment would be less than the sum of these components to
compensate the reinsurer for the high initial commission.
Since financial quota share is essentially a quota share arrangement, it will have the usual benefits
of a standard quota share arrangement. In particular, it:
 will spread risk
 will increase the capacity to accept risk
 may encourage reciprocal business
 will directly improve the solvency ratio without losing market share
 is administratively simpler than alternatives.
The insurer may also benefit from the expertise of the reinsurer, particularly in pricing, since the
reinsurer will have a significant interest in the premiums charged.

Question 4

Definition of Captive and their advantages and disadvantages

Answer 4

An insurer wholly owned by an industrial or commercial enterprise set up with the primary purpose of insuring the parent.

Advantages:
 fills gaps in cover that may not be available from the traditional insurance market
 helps manage the total insurance spend of the company and in particular to make financial plans more predictable due to the increased stability of premiums
 allows direct access to the reinsurance market
 helps focus effort on risk management
 retains profits that would otherwise have been passed to other insurers
 may gain tax or regulatory advantages, eg if the captive is set up in a low taxation offshore location.

Disadvantages:
 expenses of setting up a captive and hiring the insurance expertise needed
 capital is required to set up the captive
 regulatory approval may be required from all the countries that the multinational operates in
 risk is retained within the same group
 risk of accumulations building up due to a lack of diversity in the business written
 no access to insurers’ expertise, eg in dealing with complicated risks or claims
 setting up a captive may divert management attention from the core business.

Question 5

List the reasons why a general insurance company might want to use reinsurance

Answer 5

Reinsurance may be used by an insurer:
 to limit its exposure to risk (or spread risk) in respect of: [½]
– single risks [½]
– aggregations of single risks [½]
– accumulations [½]
– multi-class losses [½]
 to obtain additional business through reciprocity [½]
 to avoid single large losses in respect of: [½]
– single large claims [½]
– catastrophes [½]
 to smooth its results [½]
 to increase profitability by: [½]
– increasing the stability of results (and so the ability to plan) [½]
– taking advantage of cheap reinsurance [½]
 to enable it to declare profits from outstanding liabilities more quickly [½]
 to improve the solvency margin and hence reduce the risk of insolvency [½]
 to increase the capacity to accept risk, either: [½]
– singly, ie to enable it to write larger risks, or [½]
– cumulatively, ie to enable it to write more business [½]
 to obtain financial assistance to help with: [½]
– new business strain [½]
– bolstering free assets [½]
– a merger / acquisition [½]
– any other short-term cashflow needs [½]
 to get technical assistance on: [½]
– new risks [½]
– unusual risks [½]
– risks in new territories [½]
 as a supervisory condition. [½]

Question 6

Describe time and distance reinsurance (financial re.)

Answer 6

An insurer pays a single premium in return for a fixed schedule of future payments matched to the estimated dates and amounts of the insurer’s claim outgo. The purpose of such contracts was to achieve the effect of discounting in arriving at the reserves for outstanding
claims.

This is not really a form of reinsurance at all, since there is limited protection against insurance risk. [½]
It is a financial instrument that should be viewed as an investment, ie consider:
 security
 marketability
 matching by nature and term of liabilities
 expected returns. [½ each]
T&D arrangements are likely to offer poor returns, marketability and security compared with those available on other available assets. Most practical arrangements tend to be longer term
than the short-tailed property claims expected by this insurer. [1]
In practice, these arrangements may be used to improve the apparent solvency position where explicit discounting was not permitted. [½]
However, any such loopholes may have been closed, with providers now being required to discount the return payments making the transaction pointless from a solvency viewpoint. [½]
Hence, T&D is likely to be unsuitable for the insurer.

Question 7

Describe the suitability of stop loss reinsurance

Answer 7

Stop loss policies pay out when the overall losses on the account reach a certain proportion of premiums. Policies usually pay out on a proportion, say 80%, of losses up to some specified upper
limit. [1]
In theory, this is a good suggestion for the insurer. By limiting overall losses, the solvency margin could be protected from large overall losses. [½]
Unfortunately it may not be a practical suggestion. By reducing the variance in the insurer’s profitability, reinsurers are concerned that lack of management control may lead to them experiencing large losses. [½]
Hence, reinsurers may be reluctant to provide the cover.

Question 8

What are the objectives of regulating the insurance industry

Answer 8

Key objectives of regulation and supervision are to promote efficient, fair, safe and stable
insurance markets and to benefit and protect policyholders. [1]
Further objectives include to:
 enhance overall efficiency of the financial system [½]
 reduce transaction costs [½]
 create liquidity [½]
 facilitate economies of scale [½]
 contribute to economic growth [½]
 allocate resources efficiently [½]
 manage risk [½]
 mobilise long-term savings.

Question 9

What are the key activities of IAIS

Answer 9

The IAIS:
 issues global principles, standards and guidance papers [½]
 provides training and support on issues related to insurance supervision [½]
 organises meetings and seminars for insurance supervisors.

Question 10

List the capital requirements that an insurance supervisor might impose on an insurer

Answer 10

Examples of regulatory capital requirements include:
 requirement to deposit assets to back claims reserves [½]
 requirement to maintain a minimum level of solvency [½]
 the use of prescribed bases to calculate premiums, asset values and liabilities to demonstrate solvency [½]
 requirement to hold a claims equalisation reserve (eg outside the EU) [½]
 requirement for risk-based capital calculations and capital assessment analyses [½]
 requirements in respect of the capital model, eg the requirement to satisfy the ‘use test’, so that the capital model and results should be used to help manage the business.

Question 11

Describe the disadvantages to insurers of complying with the IAIS Core Principles (ICPs).

Answer 11

Disadvantages include:
 valuations may be less prudent, eg where the regulation requires assumptions to be based on actual experience, without including margins [½]
 a risk-based approach could increase the volatility of results, leading to: [½]
– more volatile distribution of profits [½]
– reduce the availability of capital [½]
 broader reporting requirements may mean that intra-group arrangements will have to be disclosed [½]
– this may bring further disadvantages, eg tax implications for arrangements that take place across different territories [½]
 increased costs of regulatory supervision, which may be passed onto insurers via increased levies [½]
 increased costs of compliance [½]
 loss of market confidence if insurers are seen not to comply with recognised best practice.

Question 12

The company is considering estimating claims by means of the chain ladder technique. Outline the points you would make in a letter to the Board explaining briefly how the chain ladder technique works, its key assumptions and whether it may give a more reliable answer than case estimates. - Part 1

Answer 12

Method:

On the basis of the pattern of claim payments from previous years, the chain ladder (CL) projects the expected total payments for outstanding claims.
The method begins by splitting past claim payments into a table divided by accident year (the year when the claim occurs) and year of payment. This will generate a triangular shaped table.

The main assumption is that the pattern of claim payments emerging from each accident year remains constant. We will then be able to estimate the claim amount. For example, the 2013
accident year, development year 6 (2013/6), from the ratio of 2012/6 to 2012/5. Projections are made on a similar basis for all years with outstanding claims. [1]
The projections can be extended beyond year 6 for those claims from the 2012 accident year which haven’t yet been settled. [½]
The CL method can also be applied to other tabulations of claims data. For example, we might tabulate claims by reporting year (rather than by accident year) in order to derive an estimate of
the outstanding reported claims. [½]
This choice will depend upon the tabulation that gives a payment pattern we believe to be stable.

Question 13

The company is considering estimating claims by means of the chain ladder technique. Outline the points you would make in a letter to the Board explaining briefly how the chain ladder technique works, its key assumptions and whether it may give a more reliable answer than case estimates. - Part 2

Answer 13

Assumptions and reliability:
We are relying on a regular pattern of claim payments to give us reliable results. In practice this might be distorted by: [1]
 changes in the mix of business from year to year [½]
 changes in policy conditions [½]
 changes in claim reporting and settlement procedures [½]
 reliability or otherwise of past data. [½]
The reliability of data can be doubtful where the amount of data is small, or there are one-off (eg catastrophic) events within past data, which should not be projected into the future. [1]
Changing inflation can have an impact on the results. However, the CL method can be adjusted to incorporate allowance for past inflation and our expectations of future claim inflation. [1]
The CL can only provide total estimates – it cannot be used as a basis for estimating claim amounts for individual claims. Further, it makes no allowance for known data about outstanding
claims. [1]
However, it is possible to apply the CL approach to tabulated data that includes estimates of claims reported to date, by year of accident and year of reporting. [½]
Providing the pattern of reporting (by estimated amount) is stable, the CL approach will provide a reliable estimate of claim amounts in relation to claims that have not yet been reported. [½]
An advantage of the CL, is that it provides an objective estimate which can be used as a check on the total estimates from the claims assessors. It may also be appropriate to consider using the CL for the first two or three years of claim development, when the number of outstanding claims is greatest. [1]
Whether the method will give a more reliable answer than produced by the case estimation will depend on how far the problems outlined in the section above are absent, and on the quality of the case estimates.

Even when a mechanical use of the chain ladder method is not appropriate (ie where there have been changes in experience), if the user is aware of the reasons why past data should not be
mechanically used as a basis for projection into the future, adjustments can be made to the standard method.

Question 14

Describe stochastic reserving method: Bootstrapping

Answer 14

Bootstrapping is 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. [½]
It involves sampling (with replacement) repeatedly from an observed data set in order to create a number of pseudo-data sets that are then consistent with the original data set. [½]
Various statistics of interest can then be derived for each pseudo-data set, and the distribution of these statistics can be analysed further. [½]
It is assumed that the sampled data are independent and identically distributed. [½]
In stochastic claims reserving we can use bootstrapping techniques to estimate the distribution of reserve predictions. [½]
This method assumes that:
 the run-off pattern is the same for each origin period [½]
 incremental claim amounts are statistically independent [½]
 the variance of the incremental claim amounts is proportional to the mean [½]
 incremental claims are positive for all development periods. [½]
This approach involves:
 obtaining a set of past claims data, split by origin / development year [½]
 back-fitting a model to the past data to find the expected claims for each cell [½]
 calculating the residual ‘noise’ present in each cell (ie actual minus expected) [½]
 sampling from this residual distribution to produce many pseudo-data sets [½]
 calculating reserve projections based on each pseudo-data set [½]
 collating the reserve projections to determine the distribution, moments and percentiles of the reserve distribution. [½]
[Maximum 6]

Question 15

Describe stochastic reserving method: Bayesian method

Answer 15

Deterministic reserving methods assume that the observed claim amounts conform to a statistical model involving parameters that have fixed but unknown values. [½]
Bayesian methods, on the other hand, assume that the parameters in the model do not have a fixed value, but themselves conform to a certain prior distribution. [½]
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. [½]
One common Bayesian method is the Bayesian version of the Bornhuetter-Ferguson model. [½]
This approach involves:
 obtaining a set of past claims data, split by origin / development year [½]
 selecting a prior distribution to model the exposure measure (which involves selecting a type of distribution, eg a gamma distribution, and assigning suitable values to the parameters, eg alpha and lambda) [1]
 determining the posterior distribution for the projection of the claims reserves (which may require a Monte Carlo approach) [1]
 using the posterior distribution to determine moments and percentiles for the claims reserves.

Refer ST7 Book Page 1305.

Question 16

Describe stochastic reserving method: Over dispersion

Answer 16

‘Over-dispersion’ refers to a distribution where the variance exceeds the mean. [½]
For the Poisson distribution, the variance equals the mean. [½]
A Poisson distribution can be considered as the starting point for modelling claims since it is the distribution underlying the Poisson process, which is the theoretical model for events that occur
completely randomly over time. [½]
In practice, claim amounts do not follow a Poisson distribution because claim amounts are not constant and claims do not occur independently. [½]
It is usually found that claims distributions are over-dispersed. [½]
One common stochastic reserving model based on this principle is the over-dispersed Poisson (ODP) model in which the variance is estimated as PHI x the deterministic estimate, where PHI > 1 is
a constant multiplier estimated from the past data [1]
If we incorporate the additional variance by making a specific assumption about the distribution involved, this results in an analytic model. [½]
An alternative approach is to bootstrap the past data.

Question 17

List the steps involved when using a stochastic approach to model the claims experience

Answer 17

 Specify the purpose of the investigation, eg rating, reserving, or planning. [½]
 Select an appropriate model structure, ie which claims to include (bodily injury, property damage etc). [½]
 Set the risk measure, eg VaR. [½]
 Determine the types of scenarios to develop and model, eg claims in a recession, changes in legislation over cover limits. [½]
 Decide which variables to include, and their interrelationships. [½]
 Collect claims and exposure data going back at least five years if possible. Find the right balance of relevance and credibility.

 Group data, eg bodily injury and property damage. [½]
 Adjust for inflation and IBNR, which could be considerable for motor business. [½]
 Adjust for any other changes, eg trends in policyholder attitudes, terms and conditions, levels of excess etc. [½]
 Estimate the parameters that should be used for each variable (ie the mathematics that specifies the behaviour of each variable): [½]
– choose a suitable density function for each of the variables to be modelled stochastically … [½]
… eg claim severity, which may depend on other variables that are often modelled stochastically (such as inflation) … [½]
– estimate the required parameters for the chosen density function(s) [½]
– ascribe values to the variables that are not being modelled stochastically … [½]
… eg claim frequencies, which may be more predictable and therefore could be modelled deterministically. [½]
 Specify correlations between variables. [½]
 Test and validate the reasonableness of the assumptions and their interactions. [½]
 Check the goodness of fit is/are acceptable and attempt a fit with different density function(s) if it is not. [½]
 Construct a model based on the chosen density function(s). [½]
 Run the model many times, each time using a random sample from the chosen density function(s). [½]
 Produce a summary of the results that shows the distribution of the modelled results after many simulations have been run. [½]
 Run the model using different distributions / parameters to check sensitivity. [½]
 Continually update the model and its parameters to remain relevant in the ever-changing environment in which the insurer operates, eg to reflect the prevailing economic, legislative and fiscal conditions.

Question 18

How to model following for capital modelling exercise: (a) Property damage motor claims

Answer 18

These claims will be primarily (if not all) classed as attritional claims. [½]
Attritional claims should be based on past experience and modelled in aggregate. [½]
Ideally, a mildly-skewed distribution would be used, eg the lognormal distribution. [½]
However, a normal distribution may be acceptable if the standard deviation is sufficiently small compared to the mean. [½]
If the class of business is so small that a distribution cannot be determined, then loss ratios may be used. [½]
Past data will need to be adjusted so that it is appropriate, eg by adjusting for inflation of mechanics’ wage levels.

Question 19

How to model following for capital modelling exercise: (b) A liability claim against a director of a large company

Answer 19

This could potentially be a very large claim. [½]
Large claims are usually modelled on a frequency-severity basis, based on past experience. [½]
The frequency might be modelled using a Poisson distribution, assuming the claim is independent of other claims. [½]
If there is anyone else involved against whom another claim could be made, eg another director at the same company, then a Poisson distribution will underestimate claims, so allowance should be made for this. [½]
The severity is likely to be modelled using a heavily-skewed distribution, such as the Pareto. [½]
Past data will need to be adjusted so that it is appropriate, eg by adjusting for changes in policy terms and conditions.

Question 20

How to model following for capital modelling exercise: (c) Earthquake claims

Answer 20

The firm’s own experience will not be appropriate because earthquakes occur too rarely and so internal data will not be valid. [½]
A proprietary model might be used to apply a set of simulated events to the insurer’s exposure.
[½]
The model should be appropriate to the insurer’s exposure, for example by geographic location and size / type of risks it insures. [½]
Allowance should be made for the likely demand surge following a catastrophe, eg the increased cost of materials to effect repairs (due to the sudden increase in demand) and the increased
demand for insurance due to policyholders’ increased awareness of the need for insurance following such an event. [½]
The model results must be tested against recent earthquakes.

Question 21

How to model following for capital modelling exercise: (d) claims made in a severe recession

Answer 21

The insurer might need to develop a bespoke model to determine the effects on different classes of business, eg: [½]
 credit insurance might experience higher claim frequency, due to the increased risk of debtor insolvency [½]
 fidelity guarantee insurance might experience higher claim rates due to the increased incidence of fraud amongst employees. [½]
Allowance should be made for correlations, eg: [½]
 with other types of risk, such as:
– operational risk, which may be higher due to the increased risk of operational
mismanagement if internal redundancies lead to staff shortages [½]
– market risk, which may be higher due to a fall in investment markets and probable increased volatility of investment returns during a recession [½]
 between different underwriting years, eg if the recession straddles more than one underwriting year [½]
 between different types of losses, eg large and attritional. [½]

It might be possible to develop a stochastic model, if sufficient historical data is available to model the likely increase in frequency and severity of claims. [½]
However, a scenario-based approach might be more likely, and will allow for a subjective view of the likely scenarios that might emerge in a recession.

Question 22

List the factors that should be considered by an insurer when considering the type and amount of reinsurance for a particular class of business.

Answer 22

 Class of business under consideration:
– size and range of risks
– volatility of experience and hence stability of profits
– the need for technical expertise.
 Size of free reserves.
 Total written premium.
 Ratio of risks in this particular class to insurer’s total business.
 Geographical regions in which risks are situated.
 Accumulations of risk:
– too much risk in one geographical region
– too many similar types of risk
– risks where claims may arise under a different class of business.
 Opportunities to find coinsurers.
 Perceived value for money.
 Availability of suitable reinsurance.
 Reinsurer’s requirement for a minimum retention.
 Financial strength of reinsurers in the market.
 Alternatives to reinsurance.
 Amount used by competitors.
 Shareholders attitude towards fluctuations in profit levels and risks in general.
 Shareholders attitude towards publishing a volatile solvency margin ratio.
 Availability of coinsurance.

Question 23

Uses of accounting ratios:

Answer 23

Ratios are used to compare accounts of different companies over many different years because they:
 are quick to produce and compare
 can indicate trends clearly, by eliminating the effects of inflation
 are flexible: different ratios can shed light on different aspects
 are robust: then can deal with different types of situation, eg:
– big company vs small company
– companies writing different types of business
– companies with different accounting layouts.

Question 24

Describe the operations of underwriting cycle

Answer 24

In the past it has been observed that insurance premium rates have varied in ways that do not reflect the underlying cost of providing the insurance. This is most common in large commercial and industrial insurance; for example that placed in the London Market, but it affects all classes of insurance.
In general, the cycle can be described in the following terms, although describing it as starting from a position of general profitability is purely arbitrary: the sequence could be entered at any point.
1. Insurance is generally highly profitable. This position is commonly known as a hard market.
2. The level of profits attracts new entrants to the market and encourages existing insurers to write more business.
3. To fill the extra capacity, premium rates are reduced to attract business.
4. Eventually premium rates fall to the extent that insurance is generally loss-making. This position is commonly known as a soft market.
5. Insurers leave the market in response to the level of losses or reduce the amount of business they write.
6. With restricted availability of insurance, premium rates increase. 7. Eventually premium rates rise to the extent that insurance is generally highly profitable.

Question 25

List possible reasons why data might be inadequate, and hence lead to uncertainty in modelling.

Answer 25

 poor data due to: [½]
– inadequate data recording procedures [½]
– poor system design – not capturing all rating factors [½]
– poor system design – not retaining a history of risks [½]
 inconsistent or incorrect data due to problems in recording: [½]
– no validation / reasonableness checks on digits, dates, amounts etc [½]
– no spot checks [½]
– no reconciliations [½]
– no cross-checks between policy and claims info [½]
– no cross-checks over different policy years [½]
 incomplete, ie data fields missing, due to: [½]
– poor systems design [½]
– poor user processes [½]
– inadequate information collected at outset by the insurer [½]
– inadequate information collected at outset by third parties
 nonexistent data for: [½]
– new class of business [½]
– new territory (may occur because of globalisation of markets) [½]
– unusual risks [½]
– infrequent claim events [½]
– certain rating groups (eg very old people, unusual classes) [½]
– extreme values (where data does not exist or is too volatile to be usable) [½]
 data not completely relevant due to changes in: [½]
– external factors (eg global weather patterns) [½]
– policy terms and conditions [½]
– underwriting philosophy [½]
– claims management processes

Question 26

Outline the factors that should be considered by the company when establishing a central computer system.

Answer 26

 Function of the system. Need input from all potential users:
– administration
– accounting
– actuarial / statistical
– management
– marketing
– other (underwriters, reinsurers, claims, investment, computing). [1]
 For private motor, there is potentially a lot of data to be processed. All of the above users will rely heavily upon the system. Their input initially is important. [½]
 Structure or outline of the system. How the system should operate, eg the branches and agents may have direct access to the system. For private motor, the company will probably want to be able to give on-line premium quotes to brokers. [1]
 Type of hardware and software to be used. [½]
 Cost of implementation. [½]
 Security, eg how the system will be monitored and who will have access to it. Data protection laws should be considered, particularly if the system is to be used by third parties. [1]
 The data that will need to be held. For private motor, we should retain all the data for individual policyholders on the system. [1]
 How files will be structured. For example, the policy and claims records might be held on separate files. [½]
 How long the data will be stored. Statistical analyses will be necessary (in due course) using the data that develops. Every effort should be made to store data indefinitely, whilst complying with any regulations over data retention.

 Capability. The system will need to be able to capture claim features such as multiple payments, nil claims and reopened claims. [½]
 The output from the system is important. Again, ask all potential users of the system. Examples of required output are: premium quotations (linked to brokers’ systems), policy documents, renewal notices, endorsement notices, management reports, marketing
statistics, run-off tables, statutory returns, accounting reports. [1½]
 Ease of use. Need to consider the computer literacy of the end users. [½]
 Implementation of the system. How the system will be developed, and by whom. How it will be tested. [1]
 When the system will be ready. This needs to be linked to the proposed launch of the new policies. [½]
 Error aversion, eg the steps that will be taken to ensure data accuracy. [½]
 Changes to the system. The system must be sufficiently robust so that future developments can be incorporated. [½]
 New company. There should be few constraints (other than cost), so the system design need not be too concerned with existing practices.

Question 27

Define model, process and parameter uncertainty and suggesting ways to reduce it.

Answer 27

(i) Model uncertainty
This arises because the model is necessarily a simplification of the real life situation. [½]
Such simplification introduces unknown bias into the model and therefore uncertainty over the validity of the results. [½]
This uncertainty can be reduced by exercising sound actuarial judgement when choosing a model. [½]
This involves selecting the model that best reflects the key features of the underlying process. [½]
If there is sufficient data then model error can be reduced by dividing data into homogeneous groups … [½]
… and by testing whether the selected model is an appropriate fit to the data … [½]
… but there is not always sufficient credible data to enable this. [½]
[Maximum 3]

(ii) Parameter uncertainty
This is the uncertainty that arises when choosing the parameters for the model. [½]
It is a result of the statistical variability in the past data used as a starting point for setting the parameters … [½]
… for example due to the presence in the past data of an unusually large claim. [½]
Parameter uncertainty can be reduced by exercising actuarial judgement when selecting parameters … [½]
… although this uncertainty can never be removed completely. [½]

(iii) Process uncertainty
This is the uncertainty that arises because of the inherent randomness of the process being modelled. [½]
It would exist even in the absence of model and parameter uncertainty. [½]
The process uncertainty is reduced if modelling large numbers of reasonably independent risks … [½]
… but will be unavoidable when modelling small numbers of correlated risks.

Question 28

Outline the rationale behind the Bornhuetter-Ferguson method for claims reserving, highlighting the difference between the deterministic and the stochastic versions.

Answer 28

The deterministic form of the Bornhuetter-Ferguson method combines two methods by calculating reserves as a weighted average of the results from the chain ladder method and the
expected loss ratio method. [½]
The rationale is that, if the run-off pattern remains unchanged, a projection of the past claims triangle should provide a good estimate of future claims.

However, this estimate can be improved if we take into account an independent estimate of the ultimate losses and apply it to the future development of losses. [½]
The independent estimate is usually calculated by applying an assumed loss ratio to the premiums, which gives an estimate of the ultimate claim amount. [½]
Deterministic reserving methods assume that the observed claim amounts (in the triangle) conform to a statistical model involving parameters that have fixed but unknown values. [½]
Once the data values have been established, the calculations could be carried out entirely mechanically, requiring no subjective judgement (although, in practice, it is likely that some
adjustments would be made in the basic chain ladder method). [½]

The stochastic form of the Bornhuetter-Ferguson method is also a weighted average of the chain ladder method and the expected loss ratio method, but it uses a Bayesian approach. [½]
With a Bayesian method, we assume that the parameters in the model do not have fixed values, but conform to a certain prior distribution. [½]
To apply this method, we combine an assumed prior distribution for the parameters with a model for the development of the claims to find the posterior distribution for the parameters. The
posterior distribution combines our initial beliefs about the parameter with the additional information provided by the data. [½]
The posterior distribution can then be used (analytically) to calculate moments and percentiles for the reserves. [½]
This method makes various assumptions, in particular, that the incremental claims are independent and identically distributed with positive values and with variances proportional to
the mean. [½]
Determining the posterior distribution often requires a Monte Carlo approach. [½]
This method has a subjective element in that a suitable prior distribution must be selected. [½]
The Bayesian (stochastic) version can be considered to have two extremes, depending on the prior distribution assumed. [½]
If a very ‘tight’ (low variance) prior distribution is assumed, the stochastic method makes very little allowance for variability in the exposure measure. [½]
In this case, a very tight posterior distribution is obtained and the results are almost equivalent to the deterministic Bornhuetter-Ferguson method. [½]
If a very ‘vague’ (high variance) prior distribution is assumed, the stochastic method largely disregards the exposure measure. [½]
In this case, a very vague posterior distribution is obtained and the results (as determined by the mean of the distribution) are almost equivalent to the deterministic method used for projecting
the claims triangle (which is usually the chain ladder method).

Question 29

Describe how you would create and use an asset-liability model to decide upon the asset strategy of the general insurer.

Answer 29

1. Investment strategy:
   We will need an objective / target, for example: ‘to maximise return subject to a probability of not meeting any statutory minimum solvency margin of no more than 1% in any of the next ten future years’. [1]
   Details of the current asset portfolio will be required, in order to check its suitability. This will be the first asset mix to be run through the model. [½]
   Investment rules / guidelines will need to be set, for example the company may impose a maximum percentage holding in equity, under particular economic conditions. [½]
   The model can be deterministic or stochastic … [½]
   … if stochastic then an economic scenario generator may be used to produce interest rates, inflation rates etc, which are then fed into the ALM. [½]

2.Assets:
In order to model assets, we need to estimate parameters for:
 the mean and variance of returns, by asset class [½]
 income and capital growth, where appropriate [½]
 interactions, eg between inflation, investment return and dividend growth. [½]

3. Liability outgo:
   To model liabilities, we need to consider the claim settlement pattern for future years. So we need:
    to look at the liabilities by class and claim type [½]
    a run-off pattern for each cohort of business mentioned above [½]
    an allowance for IBNR [½]
    an allowance for claims from business written but not yet earned [½]
    an allowance for other factors such as reopened claims. [½]
   An allowance should also be made for expenses, split by fixed, variable, commission etc. [½]
   Premiums and reinsurance recoveries should be offset from the liabilities. [½]
   An understanding of the nature, currency and term of the liabilities is required. [1]
   The interdependencies between correlated variables, both assets and liabilities needs to be modelled.
4. Future new business:
   A decision needs to be made as to whether to model expected future new business. If it is to be
   included we need to consider future volumes of business by class. [½]
5. Output:
   Whether we use a deterministic or stochastic model, we will need to run the projection many times to assess whether the asset distribution is robust to changing assumptions for example
   different levels of inflation etc. [1]
   The output will be summarised to derive information of key interest. [½]
   Having run the model, if we find that the asset category is not robust, we will need to change the distribution of assets between the main categories until we find a distribution that is appropriate.
   [1]
   This enables the analysis of optimal strategies. [½]

Question 30

Explain the value of using diagnostic tools to assess the suitability of reserving results.

Answer 30

Diagnostic tools indicate whether experience has been unusually high or low. [½]
The actuary needs then to consider whether the value of the diagnostic lies within an expected reasonable range or not. [1]
The actuary can then consider whether any unusual experience is a one-off so that no adjustment is required. [½]
If this is not a one-off then the diagnostic may be indicating that a change to the reserving methodology and/or assumptions will be required to obtain a more reasonable reserving estimate. [1]
The diagnostics provide a tool to:
 indicate which areas of the portfolio should be examined more closely [½]
 give the actuary greater confidence in the results presented [½]
 aid in the justification of the figures produced.

Question 31

Describe seven common diagnostics that might be used to examine claim amounts and claim frequency.

Answer 31

1. Loss ratios: [½]
These can be based on some or all of paid, outstanding, IBNR, incurred and ultimate claims, dependent upon the situation. [1]
They can be an indicator of changing:
 premium rate strength [½]
 claims uncertainty [½]
 inconsistencies in the model [½]
 errors in the reserving process. [½]

2.Paid to incurred claims or case estimates to incurred ratios: [½]
Changes in these diagnostics over time may reflect:
 changes in the strength of case estimates [½]
 a change in the underlying business [½]
 a change in claim settlement patterns [½]
 a change in the establishment and settlement of outstanding claims [½]
 the presence or absence of a large loss. [½]

3. Average outstanding case estimate: [½]
   This can highlight changes in the strength of case reserves. [½]
4. Ratio of IBNR to case estimates: [½]
   This diagnostic is an indicator of the level of outstanding unreported claims and their uncertainty relative to reported claims. It can help provide a feel for the reporting delays associated with the business. [1]
5. Survival ratio: [½]
   This diagnostic looks at how long a reserve or IBNR estimate will last if current paid or incurred claim development continues at a given rate. [1]
   A change in this rate can be an indicator of under or over-reserving or a change in the underlying business. [½]
6. Claim frequency and average cost per claim: [½]
   These diagnostics can be an indicator of inflationary trends in claim costs and also trends in claim frequency per unit of exposure.
7. Reinsurance to gross ratios: [½]
   If the reinsurance program does not change then we would expect ratios of gross, reinsurance and net estimates to be relatively constant. [1]
   Changes may reflect:
    changes in the amount of business retained / ceded [½]
    changes in the type of reinsurance used (eg proportional versus non-proportional) [½]
    changes to the reinsurance terms, eg deductibles, limits and reinstatements [½]
    changes in the underlying claims experience of the insurer [½]
    inconsistencies in treatment of gross and net claim estimates.

Question 32

Characteristics of a good model

Answer 32

A model should ideally meet the following requirements:
 the model being used should be valid, complete and adequately documented [½]
 the model chosen should reflect adequately the risk profile of the classes of business being modelled [½]
 the parameter values used should be accurate for the classes of business, and investments being modelled [½]
 the outputs from the model and the degree of uncertainty surrounding them should be capable of independent verification for reasonableness and should be readily communicable to those to whom advice will be given [1]
 the model should not be overly complex so that the results become difficult to interpret and communicate or the model becomes too long or expensive to run [1]
 the model should be sufficiently flexible [½]
 the model should have all parameters clearly identified and justified [½]
 the model should be structured and documented so that it can be understood by senior management and board members who do not have actuarial expertise.

Question 33

Factors affecting investment strategy

Answer 33

Accrual of liabilities in the future
Diversification
Valuation requirements Existing portfolio
Restrictions – statutory / legal / voluntary Size of the free assets (absolute / relative)
Economic outlook
Solvency requirements
Uncertainty of the liabilities
Nature of the liabilities
Tax treatment of the assets / insurer Availability of assets
Non-investible funds
Currency of the existing liabilities
Other insurers (competition)
Risk appetite
Reinsurance Expenses
Credit rating
Term of the existing liabilities
Objectives
Return (expected long-term)

Question 34

Modifications that may be required to the investment policy after a switch from lumpsum claims payment to annual payments

Answer 34

The change is likely to mean that the nature and term of the reinsurer’s liabilities will be affected, which may mean that its assets and liabilities are no longer matched (assuming that they were matched previously).
If the reinsurer expects that a material proportion of its liabilities will be affected by this change, then it may wish to adjust its investment policy. Otherwise no significant changes may be required.
If the reinsurer has considerable free assets then it may decide not to change its investment strategy and bear any mismatching risk.
It is likely that the liabilities will be more longer term in nature than previously, so the reinsurer may need to move to assets with a longer term to match its liabilities.
The precise term of the liabilities will be difficult to estimate and therefore match due to the uncertainty surrounding the future life expectancy of the claimants.
One possibility might be some form of longevity-based derivative but these might be risky and expensive.
The assets of the required term (which could be considerable) may not be available.
In addition, more of the liabilities are likely to be linked to wage inflation than previously, so we ideally need to find suitable assets to match.
We are unlikely to be able to find assets which will rise in line with wage inflation so may need to find a suitable proxy, eg RPI/CPI.
The reinsurer will also need to consider the liquidity risk to ensure that the cashflows from its assets (including any future premium income) are sufficient to enable to meet its liabilities as they fall due, particularly the annual payments

Question 35

Internal factors leading to distortion in claims data

Answer 35

1.Changes relating to the business being written, eg a change in the:  mix of business being written  underwriting standards and/or policy terms and conditions, eg limits / excesses. Weather
2. Changes in claims handling, eg a change in:  practices regarding the point at which a notified loss is formally accepted as a claim
 the basis for calculating case estimates / case reserving philosophy, eg from prudent to realistic
 the rate at which claims are processed, eg backlogs and changes in procedures will distort development patterns.
Distortions may also be caused by data errors. For example, the incorrect recording of: 
      
amounts dates
currencies claim type
policy details (so that the claims data is allocated to the wrong triangle) reinsurance recoveries (for net data)
case estimates, eg if these are not updated correctly over time or as payments are made return premiums as claims data.
Other factors that could distort claims data include a change in: 
   the frequency at which / period before non-active claims are reviewed
the speed of making claim payments, whether deliberate or due to circumstances, eg a strike by claims handlers or demand surge following a catastrophe event
the way nil and reopened claims are classified the basis on which business is written, eg losses occurring to claims made  
the average policy term or commencement date regulation
the legal environment, eg: –
– –      (ii)
court awards class actions
compensation culture / greater awareness of the ability to claim exchange rates
market wide initiatives to handle claims on a consistent basis, eg following a catastrophe event
the economic environment, eg a recession affects the level of fraudulent claims the insurer’s outwards reinsurance program (when considering net claims data) the extent of any recoveries from salvage and/or subrogation.

Question 36

External factors leading to distortion in claims data

Answer 36

Seasonality
Technological change
Investment conditions
Latent claims
Legislation
Catastrophes
Underwriting cycle
Behavioural trends
Inflation
Court awards
Weather
Awareness of the ability to claim
Global warming
Exchange rates

Question 37

Problems caused by overstating reserves

Answer 37

worsen the apparent results, leading to a loss of confidence by shareholders, brokers, reinsurers and the stock market
increase premiums where these are based on the worsened results, with the consequence of reduced market share.
reducing the apparent solvency margin, possibly causing problems with the regulators and rating agencies
lower dividends and share price and possible rights issues
tying up assets that could be applied more usefully to other projects by the insurer causing a profitable business line to be closed
causing too much reinsurance to be purchased, thereby ceding additional profit to reinsurers
increased cost and/or reduced availability of reinsurance a reduction in staff remuneration and the subsequent effect on morale
a reduction in the tax computation, at least in the short term, resulting in a higher tax bill later on.

Question 38

Problems caused by understating reserves

Answer 38

overstated profits are prematurely distributed, leading to future problems meeting liabilities
premiums will be reduced below profitable levels
the insurer pays too much tax in the short term insufficient reinsurance is purchased
reserve deteriorations are required at a later stage leading to market and regulatory concerns
a short-term improvement in the insurer’s credit rating which is subsequently reversed inappropriate investment in an unprofitable line of business profit commission will be overpaid.