The gift of insight

Using standard statistical curves to model claim severity and calculate an insurer's Individual Capital Assessment fails to incorporate underwriter knowledge. Andrew Cox explains why and explores the alternatives

The Individual Capital Adequacy Standards regime is intended to improve the insurance industry's recognition, quantification, mitigation and management of risk. Fundamental to this aim is the ability of insurers to build a financial model that genuinely reflects their understanding of the business they have taken on in the past and that they aim to accept in the near future.

All but the simplest of mono-line insurers are required to have a model of their business in order to calculate their Individual Capital Assessment. This requirement has resulted in a boom in the demand for actuarial expertise, diverting such resources away from reserving, pricing and catastrophe modelling work.

However, many in the industry, including the Financial Services Authority, have questioned whether this massive investment of time, money and brainpower has produced the hoped-for improvement in understanding insurance risk.

A key concern is that the models often fail to adequately incorporate the knowledge of an insurer's key business professionals - the underwriters.

The ideal ICA model would provide insights that could help underwriters to improve the way they manage their books of business. If underwriters do not believe in the model, the model can become an obstacle to communication between the different elements of senior management.

Claim severity challenges

The cornerstone of virtually any model of insurance risk is its treatment of claim severity, which for many classes of business is notoriously difficult to construct. In order to model claim severity, actuaries typically use one or more of the 'standard' statistical curves, such as the normal, lognormal or pareto distributions. However, experienced operators know that none of these curves tend to provide particularly good representations of the sort of claims experience that is observed in practice.

A distribution of historical liability claim sizes might resemble that shown in the diagram below. In this example, it may be that the series of 'mini-peaks' at certain claim values corresponds to typical court awards for particular types of liability claims.

But it is impossible to replicate this sort of distribution using any of the standard distributions, which will have smooth curves and a single peak. Also, it may not be possible to separate out the data for different types of claims. A more imaginative solution is needed.

More power, less imagination

The use of standard statistical curves dates back to the days of limited computing power, when actuaries and others working in general insurance used these curves on the grounds of practicality. In terms of what was possible at the time, the trade-off between accuracy and ease of use was acceptable.

Of course, the power of today's average desktop PC would have been the stuff of science fiction when most actuaries started out. So have actuaries taken advantage of the opportunity to apply more sophisticated and accurate mathematical techniques?

Arguably not - instead, it seems that many have merely belted the problem with a bigger hammer, running hundreds of thousands of simulations, while all the time relying on the same inappropriate statistical distributions.

Listen to the experts

In a few cases it is possible to fit a standard statistical curve to a reasonable range of claim sizes. But for ICA modelling, the problem often comes with the extreme claim events, for which there is likely to be little or no relevant historical data. And it is often the modelling of these extreme events that is at the heart of an ICA project.

Where past data is scarce, the modeller needs to rely heavily on other available sources of information and, in particular, the expert opinion of underwriters. It is almost certain an experienced underwriter will have a better understanding of the likely distribution of extreme claim severities than the actuary. Specifically, the underwriter will have a better idea of whether past events are indicative of what could happen in the future.

Using a standard distribution that does not reflect the underwriter's understanding is like saying that the underwriter's view is not reliable or, more likely, that the actuarial toolbox does not contain a suitable tool. The result can be an ICA model that senior management will struggle to take seriously, because it fails to reflect some of the most important available information about the insurer's true underlying risks.

Alternative techniques

Fortunately there are mathematical techniques available for bridging the gap between historic data and the underwriter's views of the future, but putting these techniques into practice requires imagination and lateral thinking. One of the surprising features of mathematical research in recent decades has been the successful application of methods used in a particular field of work to solve problems in seemingly unrelated disciplines.

One recent example is borrowing from some standard mathematical techniques used in neuroscience and artificial intelligence, and using these to produce highly flexible mathematical curves that can accurately describe past insurance claims experience and - simultaneously - reflect the underwriter's best views of future trends.

The search for new techniques enabling the accurate capture of the insurer's knowledge base, whether this is in the form of analysis of hard data or in the incorporation of softer expert opinion, should be a goal for all ambitious actuaries. The result is the ability to genuinely add value to an insurance entity by giving senior managers, underwriters and actuaries a common language for understanding and communicating the risks that the business takes on.

- Andrew Cox is a partner at Lane Clark and Peacock. The views expressed in this article are those of the author and not necessarily those of LCP as a firm.

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