Book 3 Investigations

Question 1

List, giving examples, sources of uncertainty in modelling future expense levels.

Answer 1

Uncertainty over commission / sales-related expenses
 a change in mix of business will incur a different average commission  the set-up costs and expense profile of a new channel can be difficult to predict
 brokers may change their commission structure  aggregators may have different commission arrangements

Changes in operations
 new markets  uncertain set-up costs, accommodation costs, regulatory / legal costs, etc
 off-shoring  eg uncertain wage inflation / currency fluctuations, etc
 merger or acquisition  any restructuring will incur uncertain costs  changes in business volumes / mix  leading to a different proportion of fixed / variable costs
 other one-off costs  eg the implementation of a new IT system

Changes in the environment
 economic conditions  eg salary inflation  accounting changes  eg additional compliance costs / training costs 
levies  eg payable to an industry compensation scheme  changes in the tax rate  eg insurance premium tax

Question 2

In projecting actuarial estimates, three main types of uncertainty can be distinguished. Describe each type of uncertainty, using examples to illustrate the differences between them.

Answer 2

1. Model uncertainty
   Arises from the choice of model, which is often a simplification of a very complex problem. The simplification introduces an unknown bias into the model.
   Examples:  modelling aggregate claims using a lognormal distribution, which may not be a good fit
    the model may not allow for features of the business, eg no allowance for inflation.
2. Parameter uncertainty
   Arises from inappropriate parameters, because:  of the statistical variability of the historical data  past data will never comprise all possible outcomes.
   Examples:  absence of large losses leads to mis-estimation of development pattern  unusually large events lead to overestimation of claims.
3. Process uncertainty Arises because the future outcome is inherently random.
   Present even if model selection is perfect and parameters are known with certainty.
   Example:  UPR is uncertain because a hurricane may or may not occur during the period of unexpired risk.
    A significant change in legislation with retrospective
   effect may mean that even if the model exactly reflects the underlying process as it existed in the past and it has been perfectly parameterised the actuarial estimates do not reflect actual future events.

Question 3

Outline possible sources of distortion in claims data

Answer 3

Changes in claims handling . . .
. . . changing practices in how and when a claim is recorded will distort data.
. . . including different classification of accident / reporting / payment dates
. . . or change in reserving basis / strength of claim
Claims reviews / Non Active claims
Errors in dates
Errors in amounts (paid or reserve)
Errors in codes / classes
Errors in currencies
Inaccurate case estimates . . .
. . . if these are not updated over time as new information emerges or payments
are made data will be distorted . . .
. . . or a change in strength of case reserves will distort development patterns
Seasonality
Salvage and Subrogation
Fraudulent claims
Change in T&Cs or Mix of business
Processing delays . . .
. . . backlogs or other changes in processing will distort development patterns.
Demand surge impacting claims development patterns
Large claims / CATs
Latent claims
Mis-recording return premiums as claims distorts claims data.
Changes in legislation impacting amounts and methods of payment
Regulation changes / Market Initiatives
Claims inflation . . .
. . . high levels of claims inflation or step changes will give differences in data
over time.
Changes in limits
Definition of nil claims / Reopened claims
Different allocation to class structures over time
Currency / FX issues depending on recording basis
Allocation or classification of reinsurance premiums and claims
Reinsurance programme change if considering net

Question 4

Describe the problems that can be caused by inaccurate data in a reserving exercise.

Answer 4

Fundamentally, incorrect data is likely to lead to inappropriate reserves.
Reserves can either be under or overstated as a result of data issues.
Both in aggregate and at segmental level
e.g. class of business, currency, territory, distribution channel etc
Impact on decision making giving examples
Market / Investor / Credit Rating Agency / Regulator Impact
If reserves are overstated:
Worsen apparent results leading to a loss of market confidence.
Reduce apparent solvency position leading to regulatory issues.
Reduce apparent solvency position leading to rating agency issues
Tie up assets that could be used for other projects.
Increase premiums unnecessarily leading to loss of market share.
Cause a profitable segment to be closed.
May impact assessment of RI performance (either direction)
May cause unnecessary RI purchases
May affect planning for claims handling / loss adjustment expenses
Reduce staff morale/bonuses
If reserves are understated:
Profits may be prematurely distributed . . .
. . . leading to future issues in meeting liabilities.
Future, late reserve deteriorations will cause problems with the
market/regulators.
Underpurchase of reinsurance
Too much tax is paid in the short term.
Improved rating from credit agencies (later reversed)
Premiums may be understated
with imminent profit issues
Inappropriate investment in particular lines of business

Question 5

Define parameter model and process uncertainty in an actuarial reserving model

Answer 5

Parameter uncertainty refers to the uncertainty arising from the estimation of parameters used in a model. [½]
Given that any model is an artificial of a real life situation, there will always be a certain degree of parameter uncertainty in the models that we use. [½]

Model error arises from the choice of or specification of the model. By using a simplified model to project the true underlying system, an
unknown bias is introduced into the model.

Process uncertainty is the risk inherent in writing business and settling claims in general insurance. [1]
The modelling of the number and amount of claims will vary from the true value according to random variation.

Question 6

Sources of parameter uncertainty

Answer 6

When fitting a distribution there will be uncertainty at extreme values. [1]
It is often very difficult to fit a distribution at the tails because of the lack of data at extreme values. [½]
And where there is data it may be too volatile to be usable. [½]
Assumptions will therefore have to be made from what is available which will give rise to uncertainty in the model output. [½]
Certain claim events have insufficient data to model or historic data may be deemed to be inappropriate as it is no longer directly relevant. [1]
Reserving philosophy within a company will change from time to time. [½]
For example, if claims handlers have under-reserved a case in the recent past, they may be inclined to overestimate future claims to compensate. [½]
There may also be changes in reserving philosophy following a change in senior personnel.

Large claims can be expected to have different frequency and severity distributions to attritional and catastrophe claims. [½]
They are also likely to have different development patterns. [½]
There may also be differences in development pattern based upon the type of large claim / peril. [½]
Uncertainty may also arise in how a large claim is defined, [½]
e.g. they could be defined as claims over a particular threshold, [½] or large claims may be a subjective management decision. [½]
On some occasions, there may be an absence of large reported claims which will give rise to additional uncertainty. [½]
There may also be delays in passing the data to the insurer [½]
and these delays may also differ between claims handlers. [½]

Claims inflation not as expected [1]
Inflation assumptions will often be required and the actual inflationary experience will be a significant determinant in whether the chosen reserves will be too high or too low. [1]

New distribution channels [1]
Different distribution channels will have different expense profiles. It may be difficult to predict the expense profile of a new distribution channel.
Set-up costs of a new channel must also be factored in. [½]
Planned or unplanned changes in mix [1]
Expense uncertainty also arises through a change in the relative proportions of business coming from existing distribution channels. [½]
If the mix of business changes significantly the development pattern is likely to change and in an unpredictable way.

Question 7

Sources of Model uncertainty

Answer 7

Programming error… [1]
Simulation error/too few simulations… [1]
The output of a stochastic model will be heavily influenced by the number of simulations carried out: [½]
the greater the number of simulations, the greater the accuracy of the output.
However, large and complex stochastic models can take a considerable amount of time to run. [½]
If the modeller has severe time constraints, there may have to be a sacrifice in the number of simulations or in the complexity built into the model. [½]
Incorrect dependencies… [1]
A number of the variables in the model will be correlated with one another; for example, interest rates and claims inflation. [½]
Incorrect distributional assumptions in modelling reserve uncertainty… [1]
It is sometimes necessary to calculate a range of possible values for a reserve in which case distributional assumptions will be required.

Question 8

Sources of process uncertainty

Answer 8

• Process uncertainty is the risk inherent in writing business and settling claims in general insurance. [½]
• …The modelling of the number and amount of claims will vary from the true value owing to random variation. [½]
• Change in development patterns [½]
• Inherent uncertainty in individual claims [½]
• Demand surge [½]
• Booked reserves different to best estimate: Process uncertainty in reserving risk may exist due to reserves in the model not being the same as the best estimates at that point in time. This could impact the reserve distribution and could be caused by: [1]
• …Using projected best estimates rather than actuals [½]
• …Using booked reserves rather than best estimates [½]
• Climate change [½]
• Broker mergers, aggregators, or new distributions channels may result in uncertainty in expected commission in underwriting risk
• Increased use of profit share arrangements: Changes in profit sharing arrangements will impact both the expected results and other points within an underwriting classes expected loss distribution [½]
• Changes in claims handling procedures may introduce process uncertainty in reserve risk [½]
• Bodily injury claims [½]
• Changes in third party behaviour could introduce process uncertainty in any risk area depending on where the insurer uses third party [½]
• Changes in legislation: Liability products tend to be heavily impacted by legislation changes and so this will be a key source of process uncertainty [½]
• For example the change in Ogden rate for bodily injury claims had a big impact of many motor insurers capital.
• Offshoring [½]
• Uncertainties in expenses such as levies could introduce process uncertainty in underwriting risk [½]
• The position in the economic cycle and the economic conditions will impact multiple risk areas as: [1]
• …It may mean that assets are less liquid resulting in difficulties settling claims. [½]
• …This is difficult to capture in a capital model as they generally look at specific time points rather than being continuous [½]
• …Liability lines of business are generally longer tail and so are more impacted by the discount rate which will be driven by economic variables [½]
• Loss ratio results for liability lines tend to be very much affected by the economic situation [½]
• …Particularly classes such as D&O and E&O which will tend to receive many more claims in adverse economic times [½]
• Traditional monetary policy now not as effective at controlling the economy [½]
• New types of investments [½]
• Globalisation of investment markets will introduce process uncertainty in market risk. [½]
• Influence of other investment markets [½]
• Globalisation of insurance markets [½]
• Regulation arbitrage [½]
• New Markets: If liability is written in new markets, this is likely to result in increased process uncertainty due to the lack of available information that is likely to be available specific to this market (insurance risk) [½]
• If the company is writing in multiple countries the exchanges rates are likely to have an impact, particularly due to their longer tailed nature. [½]
• Changes in business mix [½]
• New latent claims