Uncertainty
- The value of insurance liabilities is uncertain. Sources of this uncertainty include, but are not limited, to the following:
(a) the valuation model or models adopted for analysis and projection are unable to fully capture the complexities of an actual claim process;
(b) fluctuations in observed claim experience result in uncertainty in selecting suitable assumptions for the valuation model;
(c) errors in the claim data result in errors in selecting assumptions;
(d) future economic and environmental factors that impact upon future claim payments are uncertain;
(e) projected payments relating to Premiums Liabilities relate to events that are yet to occur; and
(f) there is uncertainty in the projected payments, even if the true claim experience assumptions could be found for a perfect model.
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Although the analogy is not exact, it is useful to think of the true value (which can only be known, in hindsight, after all claims are settled and, even then, only imperfectly) as a random variable, drawn from a probability distribution of possible outcomes. This notional probability distribution has an expected value and shape that can be quantified in terms of its second and higher moments. The aim of the actuarial estimation process is to arrive at an estimate of the notional expected value. It is also possible to think in terms of this estimate having a standard error, skewness, etc.
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The actuary is required to quantify the uncertainty, which will generally require use of one or more of the following:
(a) statistical analysis;
(b) sensitivity analysis, changes to claim experience assumptions or the valuation models;
(c) comparison with previous valuations;
(d) analysis of scenarios; and
(e) judgement.
- In this quantification, it may be useful to think in terms of two components of uncertainty, independent and systemic:
(a) Independent variation arises out of factors that have an isolated impact on individual policies or claims. If there is a sufficient body of data, it is susceptible to rigorous statistical analysis. It can be controlled by diversification and reinsurance. Its relative importance is inversely proportional to the square root of the size of the portfolio; and
(b) Systemic uncertainty arises out of factors that affect the portfolio as a whole. Because of the nature of many of these factors, it is not easily susceptible to statistical analysis, if at all. Even where a reasonable body of past data is available for analysis, it can often be argued that the conditions observed in the past are unlikely to continue unchanged in the future. Most assessments of systemic uncertainty rely heavily on actuarial judgement.
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The above split is, of course, an oversimplification. Actual experience is driven by factors that range between these two extremes. Most real world variables are partially correlated, rather than perfectly correlated or perfectly independent. The split does, however, provide a useful framework for discussing and assessing overall uncertainty.
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GPS 210 requires the actuary to estimate uncertainty in terms of the 75th percentile, and half the coefficient of variation, of the net insurance liability, excluding investment and operational risks, and assuming a matched portfolio of sovereign risk assets. The risk of reinsurance default should be included in this assessment (see paragraph 24).
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Where classes of business are valued separately, uncertainty should be assessed for each class separately, as if that class stands alone. The actuary should initially assess the 75th percentile of the combined Outstanding Claim Liabilities and Premiums Liabilities. This should then be split between Outstanding Claim Liabilities and Premium Liabilities. In the absence of any better basis, it is acceptable to assume this split is in proportion to the respective central estimates. If the actuary is concerned that the distribution of the total liability is particularly skewed, the actuary should form a view as to whether the 75th percentile is less than half the coefficient of variation above the mean and substitute the higher value. For less extreme distributions, while it may be helpful, an explicit estimate of the coefficient of variation is not required.
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While it may be helpful for the actuary to form a view as to the approximate shape of the notional probability distribution, this is not necessary. All that is required, is for the actuary to adopt a figure which is intended to be the higher of the 75th percentile and half the coefficient of variation more than the mean. Where the actuary does work in terms of a particular notional probability distribution, this should be described in the report, along with the reasons why it is considered appropriate. Where this is not done, the actuary should discuss the reasoning behind the figure chosen.
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As it will be necessary to allow for the benefits of diversification across the company as a whole, the actuary should also discuss the way in which the uncertainties, of the class of business being valued, might interact with the other business of the company. This can be done in terms of a discussion of the independent and systemic components of the assessed uncertainty. Where this is not feasible or considered appropriate, the actuary should indicate the extent of uncertainty, as if the insurance liabilities for the class of business being assessed were of the size of the likely total insurance liabilities for the company as a whole.
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The actuary should describe, in a qualitative fashion, the key drivers of uncertainty for the class of business or portfolio being valued. Material changes in these key drivers, or uncertainty generally, since the previous valuation, should be discussed and, if appropriate, quantified.