SP7 CHAP 18 Reserving Uncertainty PDF

# 18 Reserving Uncertainty ## Syllabus Objectives - Uncertainty and its communication in reserving. - "Best estimate" reserve. - Approaches to estimating ranges of reserves: - stochastic models - scenario tests - use of alternative sets of assumptions. - Issues to consider when communi...

# 18 Reserving Uncertainty ## Syllabus Objectives - Uncertainty and its communication in reserving. - "Best estimate" reserve. - Approaches to estimating ranges of reserves: - stochastic models - scenario tests - use of alternative sets of assumptions. - Issues to consider when communicating reserve ranges and uncertainties. ## 0 Introduction Reserving is not an exact science. This chapter discusses techniques that guide actuarial judgment for setting a reserve estimate. For many types of business, the initial calculation of a reserve estimate is based mostly on quantitative techniques. Later, actuarial judgment is used to refine the estimate. This judgment can be based on: - qualitative assessment of the state of the underwriting cycle - changes in the mix of business - changes in distribution sources - changes in policy terms and conditions Inevitably, the ultimate value of the quantity is likely to differ from our original estimate. This presents two important issues: - We must be clear what we mean by a single point estimate (or best estimate) of an outstanding liability. - We should attempt to quantify the degree to which the eventual outcome may diverge from the point estimate and the likelihood of such divergence (that is, quantify the uncertainty). This chapter describes what is usually meant by a 'best estimate' reserve and describes techniques used to help quantify the uncertainty in eventual outcomes. ## 1 Sources of Uncertainty There are a number of sources of uncertainty in actuarial estimates. ### Question From your memory of earlier in the course, write down as many factors as you can that contribute to reserve uncertainty. ### Solution #### Sources of Process Error - General claims uncertainty: - Inherent uncertainty in individual claims (amount, frequency and timing) - Changes in mix of business - Demand surge - Normal retirement - Internal sources: - Changes in business mix - Booked reserves different to best estimate - Uncertainty over commission and other sales-related expenses - New markets - New types of investment - Systematic sources: - The economic environment - The insurance cycle #### Sources of Parameter Error - The data used: - Poor quality data - Inconsistent data - Incomplete and non-existent data - Incorrect modelling assumptions, e.g. - Correlations in the model - Statistical Distributions - Change in case estimate reserving philosophy - Planned or unplanned changes in mix - Particularly large/unusual risks: - Large claims - Catastrophes - Latent claims - Inadequate data supplied by third-party claims handlers - Format of data - Claims inflation not as expected - Uncertain sales-related expenses, commission, new distribution channels, etc. #### Sources of Model Specification Error - Model error - Programming error - Simulation error/too few simulations Uncertainty in actuarial estimates can broadly result from three areas: model, parameter and process. ### 1.1 Model Uncertainty Model uncertainty is the risk that an inappropriate model has been used in the estimation process. This arises because actuarial models are often a simplification of a very complex (and unknown) underlying system. By using a simplified model to project the true underlying system, we are introducing unknown bias into the model. A common example of this in actuarial modelling is the use of parametric distributions for outstanding claims reserves (like the log-normal distribution). The complexity of the claims process and the factors influencing it make it unlikely that the real distributions match simple statistical models. ### 1.2 Parameter Uncertainty Parameter uncertainty refers to the uncertainty in determining the parameters for an actuarial model. This usually results from the statistical variability present in the historical data used to estimate the parameters. ### 1.3 Process Uncertainty If a process is assumed to be inherently stochastic, the future outcome will be uncertain because of the randomness of the process and the fact that many of these events have not yet occurred. ## 2 Best Estimate Reserves We normally define the best estimate as the actuary's view of the mean or expected value (also called the unbiased probability) of the eventual outcome. ### Question Explain why this is the case. ### Solution Because there is great uncertainty over the future number, size and timing of claim amounts. Instead, the actuary will estimate a reserve value using an approach that is intended to derive a mean or expected outcome. The actuary will not be certain that the value derived does equate to a mean value but will ascribe the term 'best estimate' to the determined value to convey the 'type' of estimate that the actuary is deriving. It should also be noted that the actuary will be calculating a sample mean as an approximation to the population mean. This means that a best estimate should allow for information that is available to the actuary but may not be reflected in the underlying data yet. ## 3 Estimating the Range of Possible Outcomes There are methods that allow us to quantify some of the uncertainty in the outstanding reserves. ### Exam Tip The Core Reading for Subject SP7 draws occasionally on professional guidance such as the Technical Actuarial Standards. It may therefore be useful preparation for the exam if you familiarise yourself with the content of professional guidance issued by the Institute and Faculty of Actuaries on general insurance. ### 3.1 Stochastic Models One way to quantify the uncertainty in a reserve estimate is to construct a stochastic model of the claim development process. This is a generalized linear model (GLM) applied to claims triangles where the form is chosen so that the mean (or best estimate) reserve is equal to that resulting from a deterministic basic chain ladder method. ### Question List the key assumptions underlying this method. ### Solution The key assumptions used when bootstrapping the ODP are: - The run-off pattern is the same for each origin period (as for the chain ladder) - Incremental claim amounts are stochastically independent. - The variance of the individual claim amounts is proportional to the mean. - Incremental claims are positive for all development periods. ### 3.2 Alternative Sets of Assumptions Another way to quantify the uncertainty in a reserve estimate is to estimate the reserve using parameters different to those of the best estimate. The resulting spread of reserve estimates provides a range around the best estimate reserve. ### Question Suggest what type of uncertainty we are allowing for if we use alternative sets of assumptions for a deterministic model. ### Solution Parameter uncertainty. ### 3.3 Scenario Testing A third way to quantify the uncertainty in a reserve estimate is scenario testing. ### Question A company writes employers' liability business. Give an example of: - A financial risk - An operational risk - A legal risk That might have an impact on the company's outstanding liabilities. ### Solution - Financial risk: failure of a capital provider, failure of assets. - Operational risk: mismanagement of the portfolio, poor data recording and lax claims handling. - Legal risk: a court precedent increases the level of claims. ## 4 Communicating Best Estimates ### 4.1 Communicating Best Estimates The commonly used phrases 'best estimate' or 'central estimate' can mean different things to different people. ### 4.2 Communicating Uncertainty For many purposes, it will be appropriate to give an estimate of the uncertainty surrounding the best estimate by giving a margin or range. A range of reserve estimates can help key stakeholders understand the uncertainty inherent in the business. ### Question List the four sources of uncertainty in a reserving model. ### Solution Specification error, selection error, estimation error and process error. ## 5 Conclusion In summary, all actuaries must comply at all times with relevant ethical and technical professional guidance, as issued and revised from time to time by their profession and regulators. This should by now be of no surprise to you and the Institute and Faculty of Actuaries is pretty unbending in this respect (note the use of the word 'must' in the above paragraph). If an actuary does not have the knowledge / expertise required (or access to others who do have it) in order to carry out a piece of work, they should refuse to act. ## Chapter 18 Summary - The actual ultimate claims amount will almost certainly differ from our estimate. We should: - Clearly define what we mean by our single point (or best) estimate. - Attempt to quantify the likely divergence from this estimate. - Uncertainty is a result of: - Model uncertainty - simplifications in the model used to project an underlying complex system introduce bias. - Parameter uncertainty - due to difficulties in setting appropriate parameters for the future from the past data. - Process uncertainty - even if the model and parameters were perfectly selected this would still exist due to the inherent randomness of the claims process. - A best estimate is normally defined as the actuary's view of the mean or expected value of the eventual outcome. However it will include areas of uncertainty (model, parameter, process). - The actuary should make clear what scenarios have been included / excluded in deriving the best estimate. - The risk margin or range gives an estimate of the uncertainty surrounding the best estimate. - Three methods may be used to estimate the range of possible outcomes: - Stochastic models - Alternative sets of assumptions - Scenario testing. - Other types of ranges that might be used by actuaries include: - Range of possible outcomes - Range of reasonable / probably / plausible outcomes. - In Solvency II the best estimate is characterised as: - A point estimate - Not inherently optimistic or pessimistic - Based on sound and appropriate actuarial or statistical techniques - Based on current and credible information - Nothing is said in the requirements about the skewness of the underlying distribution or its volatility. ## Chapter 18 Summary Continued ### Stochastic Models - Stochastic models may involve the use of the ODP model or Mack model. - Results may not be reasonable if: - Past data is affected by one-off events. - Volatility in past claims development is not a good indicator of underlying process uncertainty. ### Alternative Sets of Assumptions - This estimates reserves using sets of parameters different to that of the best estimate. - It should allow for correlations between assumptions. - Advantages are: - Easy to perform - Allows judgement to be exercised. - Disadvantages are: - Does not estimate the distribution of future outcomes - Ignores model uncertainty - Does not allow for process uncertainty if using a deterministic model. ### Scenario Testing - This examines the likely impact of catastrophic events, used to examine the top limit of the range of possible outcomes. In extreme conditions areas of uncertainty may become more correlated than normal. - Scenarios can be derived: - On a historical event - From judgement, thinking up a hypothetical event - From the results of a stochastic model. ### Communicating Uncertainty - Uncertainty can be communicated by using words or numbers. - When communicating the uncertainty of the results, an actuary should: - Ensure stakeholders understand the level of uncertainty. - Take account of the audience's knowledge. - Be consistent with vocabulary used by other professionals, and explain terms. - Emphasise the bigger issues. - Explain what has been allowed for in the best estimate, and what has not. - Emphasise the unusual issues. - Comment on the uncertainty in the context of the scope and purpose. - Avoid misunderstandings. - Any reserving calculations must take account of the local reserving regulations and accounting standards.