Important Flashcards

Question

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

Answer 1

 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

Answer 2

 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.

Answer 3

(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.

Answer 4

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).

Answer 5

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]

Answer 6

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.

Answer 7

``` 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.

Answer 8

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.

Answer 9

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)

Answer 10

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

Answer 11

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.

Answer 12

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

Answer 13

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.

Answer 14

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.

Important Flashcards

(38 cards)