Category: Actuarial Science

In a previous post I discussed the M4 conference and what my key takeaways were. In this post I plan to focus the discussion on insurance, and then specifically on actuarial work, and think about what the advances in time series forecasting might mean for actuaries and other professionals in insurance.

This post starts off by discussing the traditional time series forecasting problem, where it appears in the context of insurance, and how insurers could benefit from recent advances, and then narrows in to focus on actuarial work.

Let’s quickly cover what is meant by time series forecasting. Quite often, the only data that is available for a problem consists of past values that a series took, measured at regular points in time In other words, associated variables which would help to explain the past values of the series, are not available, and the exercise needs to be informed only by the past values of the series. For example, one might have data on the number of various insurance products sold monthly for the past five years (in this case, associated variables such as number of salespeople or advertising spend might not be available), and to understand revenue, one might need to forecast the number of products that will be sold over the next quarter or year.

Some more examples of this are given in a fantastic online book on forecasting by Rob J Hyndman and George Athanasopoulos over here. I would recommend this book to anyone interested in time series forecasting!

Insurance and forecasting 

Compared to more traditional industries, insurance is interesting in that there is no physical product being sold, and insurers do not need to maintain or forecast inventories. Having said that, the familiar time series forecasting problem pops up in the context of insurance in other areas, for example:

• Forecasting the number of sales or claims and the associated resourcing requirements
• Forecasting revenue, losses, expenses and profits

Perhaps surprisingly, revenue forecasts play a major role in determining the capital requirements of insurers under Solvency II, which is the European insurance legislation, as well as in SAM, which is the South Africa variation. In fact, part of the capital requirements for insurance risk are often directly proportional to forecast premiums, see, for example, Article 116.3.a of the Solvency II Directive. 

So, besides for insurers, regulators around the world also have an interested in ensuring that revenue forecasts are accurate and advances in time series forecasting, such as those at the M4 conference, should see wider applications in insurance. One advance to consider is Microsoft’s extensive use of machine learning to determine revenue forecasts, as described in this paper , by Jocelyn Barker and others. At the M4 conference (and in the paper) Jocelyn noted that these forecasts are used for widely from providing Wall Street guidance to managing global sales performance. 

Some of the other ideas that could also be of benefit, that were expressed at the M4 conference, and are now clearly established in the time series literature are understanding:

• when to make changes to statistical forecasts (summary here)
• the value of aggregating forecasts (insightful presentation from Bob Winkler at M4 on the topic is here) from different methods

A peculiarity of insurance forecasting is that often insurance professionals will not aim to forecast the actual value of losses and expenses, but rather will focus on ratios that express these quantities in terms of revenue (or a close proxy to revenue). For example, if one wants to forecast losses, then one would try to forecast loss ratios, which express how many cents are paid in losses for every dollar of revenue. In the next section, I will discuss how these ratios are often currently forecast in insurance companies. 

Forecasting in Actuarial Work

For the main topic of this post, I want to examine the work that actuaries do for insurers, that often consists of, or contains forecasts of some kind.

In life insurance, these forecasts are often the key variables underlying pricing and reserving such as:

• Mortality
• Morbidity
• Withdrawal or lapse rates
• Expenses

In P&C insurance (or general or short-term if you are in the UK or South Africa), these forecasts are often comprised of:

• Loss ratios
• Frequency rates and average cost per claim
• Premium rates

• Claims development patterns

As an aside, not so long ago, these lists would have included investment returns, but a large swathe of the actuarial profession has more or less adopted market consistent valuation practices, which dictate that all cashflows should be valued like bond cashflows, with the implication that investment returns can simple be read off from market yield curves. One currently controversial discussion here is the valuation of no negative guarantees on reverse mortgages in the UK, see here from Dean Buckner and Kevin Dowd.

A common assumption that is made for some of these variables is that whatever experience has occurred over the past few years will repeat itself in the future – in time series jargon, actuaries often use so-called “naive” forecasts (please read the conclusion though, where I note that this is not always the case). Here are some examples of naive forecasts in current actuarial work:

• When determining (P&C) claims reserves, an allowance must be made for the costs of managing claims (to be precise, here I refer to claims department and associated costs, or ULAE), in addition to the cost of indemnifying policyholders. The South African SAM regulations allow actuaries to forecast these costs on the basis of the average claims management costs over the past two years/
• Also on P&C reserving, a very common approach to determining claims development patterns (which are used then to forecast the extent of the outstanding claims that are still to be reported) is to rely on  averages of recent experience. 
• Mortality analysis often consists of comparing an assumed mortality table to recent experience. The assumed mortality table is then adjusted to match the recent experience more closely, and only rarely will a trend over time be allowed for. 
• When pricing P&C insurance with a GLM, a dataset of recent claims experience is used to derive factors which define how different policies are likely to perform. For example, how much more likely are claims if the policyholder is a new driver, compared to an experienced driver. These factors are most often based on the recent past, with no allowance for trend over the years.

In all these examples, the recent past is taken as representative of the future. The reasons for this are probably a general lack of sufficient data to do better, and the difficulties in specifying a suitable model that can capture these changes over time adequately. However, as data quality (and quantity) improves, and especially, as the options for modelling increase (for example, using neural nets instead of GLMs), I think there are ample opportunities to improve on some parts of current practice. 

Two potential paths to achieve this stand out for me from the M4 conference:

• One way to improve forecasts is to come up with a smart way of ensembling multiple models (as opposed to coming up with new, more complicated models), as done by the runners up to the M4 competition (link). Of course, this needs to be done in a scientific manner, and very little research has been performed on how this could be achieved on traditional actuarial models. The advantage of this approach is that the building blocks remain the same traditional models, and a meta-model works out which of these models is best and when.
• Another way is more or less to forget about model specification, and let a neural net find an optimal model automatically, as was done in Slawek Smyl’s winning solution (link). To do this, one generally needs more data than in traditional modelling approaches, but the results can be impressive. I particularly favor this latter approach, and for examples of applications to population mortality forecasting and claims reserving, I would point to two recent papers I co-authored that are up on SSRN that demonstrate this approach:
  • Mortality forecasting
  • Claims reserving

Having noted some of the above areas that can be improved, it is important to end by stating that often, data simply isn’t available to do much better than the most simple forecasts, and, indeed, in cases where the data is available, actuaries will try use more sophisticated modelling. One example is mortality improvement modelling, generally undertaken by providers of annuities and other products exposed to longevity risk, where actuaries apply mortality models from both the actuarial and demographic “schools”, most often to population level data. Another example is claims reserving, where there is increasing attention being placed on developing reserving models that allow for trends in claims development assumptions over time, though I have not yet seen one of these in practice. 

In conclusion, I think it is an exciting time to be involved in actuarial work and insurance more broadly, and I look forward to seeing how advances made in other areas will influence the insurance industry.